%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN004-3 : 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 : n008.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 07:31:44 AM UTC 2026
% Result : Unsatisfiable 25.29s 3.80s
% Output : CNFRefutation 25.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of clauses : 36 ( 25 unt; 0 nHn; 13 RR)
% Number of literals : 49 ( 22 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_x_divide_zero_is_x,negated_conjecture,
divide(a,zero) != 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$uequal'(X0,X1) ) ).
cnf(c0,plain,
divide(a,zero) != a,
inference(clausification,[status(esa)],[prove_x_divide_zero_is_x]) ).
cnf(c1,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
cnf(c2,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c3,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c4,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c5,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c6,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d1,plain,
( ~ 'less$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d2,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[c1,c5]) ).
cnf(d3,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)),
inference(superposition,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(d5,plain,
'less$uequal'(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( 'less$uequal'(divide(X0,X0),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
divide(zero,zero) = zero,
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d10,plain,
zero = zero,
inference(demodulation,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
'less$uequal'(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( 'less$uequal'(divide(X0,divide(X0,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d10,d15]) ).
cnf(d17,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n008.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Fri Sep 25 15:56:54 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.29/3.80 % SZS status Unsatisfiable for theBenchmark.p
% 25.29/3.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------