%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN004-5 : 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 : n003.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 12.56s 2.96s
% Output : CNFRefutation 12.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 27 ( 18 unt; 0 nHn; 11 RR)
% Number of literals : 40 ( 39 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_divide_x_is_zero,axiom,
divide(X0,X0) = zero ).
cnf(prove_x_divide_zero_is_x,negated_conjecture,
divide(a,zero) != a ).
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X0,X1),X0) = zero ).
cnf(quotient_property,axiom,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero ).
cnf(zero_is_smallest,axiom,
divide(zero,X0) = zero ).
cnf(divide_and_equal,axiom,
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ) ).
cnf(c0,plain,
divide(X0,X0) = zero,
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c1,plain,
divide(a,zero) != a,
inference(clausification,[status(esa)],[prove_x_divide_zero_is_x]) ).
cnf(c2,plain,
divide(divide(X0,X1),X0) = zero,
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c3,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c4,plain,
divide(zero,X0) = zero,
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c5,plain,
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[divide_and_equal]) ).
cnf(d0,plain,
( divide(X0,divide(X0,X1)) != zero
| divide(X0,X1) = X0
| zero != zero ),
inference(superposition,[status(thm)],[c2,c5]) ).
cnf(d1,plain,
divide(zero,zero) = zero,
inference(superposition,[status(thm)],[c4,c2]) ).
cnf(d2,plain,
zero = zero,
inference(demodulation,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( divide(X0,divide(X0,X1)) != zero
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( divide(X0,zero) != zero
| zero = X0
| zero != zero ),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d5,plain,
( zero = X0
| divide(X0,zero) != zero ),
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
divide(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)) = zero,
inference(superposition,[status(thm)],[c4,c3]) ).
cnf(d7,plain,
divide(divide(divide(X0,divide(X0,zero)),zero),zero) = zero,
inference(superposition,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
( zero = divide(divide(X0,divide(X0,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d2,d8]) ).
cnf(d10,plain,
( zero = divide(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d2,d10]) ).
cnf(d12,plain,
( divide(X0,zero) = X0
| zero != zero ),
inference(superposition,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 15:57:52 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.56/2.96 % SZS status Unsatisfiable for theBenchmark.p
% 12.56/2.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------