%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN005-5 : 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 : n013.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 07:31:45 AM UTC 2026
% Result : Unsatisfiable 20.73s 5.51s
% Output : CNFRefutation 20.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of clauses : 40 ( 29 unt; 0 nHn; 18 RR)
% Number of literals : 55 ( 54 equ; 17 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_divide_b_is_zero,hypothesis,
divide(a,b) = zero ).
cnf(b_divide_c_is_zero,hypothesis,
divide(b,c) = zero ).
cnf(prove_transitivity_of_divide_to_zero,negated_conjecture,
divide(a,c) != zero ).
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(a,b) = zero,
inference(clausification,[status(esa)],[a_divide_b_is_zero]) ).
cnf(c1,plain,
divide(b,c) = zero,
inference(clausification,[status(esa)],[b_divide_c_is_zero]) ).
cnf(c2,plain,
divide(a,c) != zero,
inference(clausification,[status(esa)],[prove_transitivity_of_divide_to_zero]) ).
cnf(c3,plain,
divide(divide(X0,X1),X0) = zero,
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c4,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c5,plain,
divide(zero,X0) = zero,
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c6,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
| X0 = divide(X0,X1)
| zero != zero ),
inference(superposition,[status(thm)],[c3,c6]) ).
cnf(d1,plain,
divide(zero,a) = zero,
inference(superposition,[status(thm)],[c0,c3]) ).
cnf(d2,plain,
zero = zero,
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( divide(X0,divide(X0,X1)) != zero
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( divide(X0,zero) != zero
| X0 = zero
| zero != zero ),
inference(superposition,[status(thm)],[c5,c6]) ).
cnf(d5,plain,
( divide(X0,zero) != zero
| X0 = 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)],[c5,c4]) ).
cnf(d7,plain,
divide(divide(divide(X0,X0),divide(X1,X0)),zero) = zero,
inference(superposition,[status(thm)],[c3,c4]) ).
cnf(d8,plain,
divide(divide(divide(X0,X0),zero),zero) = zero,
inference(superposition,[status(thm)],[c5,d7]) ).
cnf(d9,plain,
( divide(divide(X0,X0),zero) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
divide(divide(X0,X0),zero) = zero,
inference(resolution,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
( divide(X0,X0) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
divide(X0,X0) = zero,
inference(resolution,[status(thm)],[d2,d11]) ).
cnf(d13,plain,
divide(divide(divide(X0,divide(X0,zero)),zero),zero) = zero,
inference(superposition,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( divide(divide(X0,divide(X0,zero)),zero) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(resolution,[status(thm)],[d2,d14]) ).
cnf(d16,plain,
( divide(X0,divide(X0,zero)) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[d2,d16]) ).
cnf(d18,plain,
( X0 = divide(X0,zero)
| zero != zero ),
inference(superposition,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
X0 = divide(X0,zero),
inference(resolution,[status(thm)],[d2,d18]) ).
cnf(d20,plain,
divide(divide(divide(X0,c),zero),divide(divide(X0,b),c)) = zero,
inference(superposition,[status(thm)],[c1,c4]) ).
cnf(d21,plain,
divide(divide(X0,c),divide(divide(X0,b),c)) = zero,
inference(demodulation,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
divide(divide(a,c),divide(zero,c)) = zero,
inference(superposition,[status(thm)],[c0,d21]) ).
cnf(d23,plain,
divide(divide(a,c),zero) = zero,
inference(demodulation,[status(thm)],[d22,c5]) ).
cnf(d24,plain,
divide(a,c) = zero,
inference(demodulation,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[c2,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:55:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.73/5.51 % SZS status Unsatisfiable for theBenchmark.p
% 20.73/5.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------