%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:10:40 AM UTC 2026
% Result : Unsatisfiable 13.15s 12.45s
% Output : CNFRefutation 13.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 13 unt; 7 nHn; 23 RR)
% Number of literals : 56 ( 0 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry,axiom,
( equalish(X1,X0)
| ~ equalish(X0,X1) ) ).
cnf(equality_preserved_over_times,axiom,
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ) ).
cnf(not_less_and_equal,axiom,
( ~ equalish(X0,X1)
| ~ less(X0,X1) ) ).
cnf(numbers_either_less_or_equal,axiom,
( less(X1,X0)
| equalish(X1,X0)
| less(X0,X1) ) ).
cnf(number_not_less_than_itself,axiom,
~ less(X0,X0) ).
cnf(multiply_lemma,axiom,
( less(multiply(X0,X2),multiply(X1,X2))
| equalish(X2,n0)
| ~ less(X0,X1) ) ).
cnf(b_not_less_than_a,hypothesis,
~ less(b,a) ).
cnf(b_times_c_less_than_a_times_c,hypothesis,
less(multiply(b,c),multiply(a,c)) ).
cnf(prove_c_is_0,negated_conjecture,
~ equalish(c,n0) ).
cnf(transitivity_of_less,axiom,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ) ).
cnf(c1,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry]) ).
cnf(c3,plain,
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[equality_preserved_over_times]) ).
cnf(c4,plain,
( ~ equalish(X0,X1)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[not_less_and_equal]) ).
cnf(c5,plain,
( less(X1,X0)
| equalish(X1,X0)
| less(X0,X1) ),
inference(clausification,[status(esa)],[numbers_either_less_or_equal]) ).
cnf(c6,plain,
~ less(X0,X0),
inference(clausification,[status(esa)],[number_not_less_than_itself]) ).
cnf(c8,plain,
( less(multiply(X0,X2),multiply(X1,X2))
| equalish(X2,n0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[multiply_lemma]) ).
cnf(c9,plain,
~ less(b,a),
inference(clausification,[status(esa)],[b_not_less_than_a]) ).
cnf(c10,plain,
less(multiply(b,c),multiply(a,c)),
inference(clausification,[status(esa)],[b_times_c_less_than_a_times_c]) ).
cnf(c11,plain,
~ equalish(c,n0),
inference(clausification,[status(esa)],[prove_c_is_0]) ).
cnf(c18,plain,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less]) ).
cnf(d0,plain,
( ~ less(X3,X0)
| equalish(X1,n0)
| less(multiply(X3,X1),X2)
| ~ less(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d1,plain,
( less(multiply(X0,c),multiply(a,c))
| ~ less(X0,b)
| equalish(c,n0) ),
inference(resolution,[status(thm)],[d0,c10]) ).
cnf(d2,plain,
( less(multiply(X0,c),multiply(a,c))
| ~ less(X0,b) ),
inference(resolution,[status(thm)],[c11,d1]) ).
cnf(d3,plain,
~ less(a,b),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( less(a,b)
| equalish(a,b) ),
inference(resolution,[status(thm)],[c5,c9]) ).
cnf(d5,plain,
( equalish(multiply(X1,X2),multiply(X0,X2))
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d6,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d7,plain,
~ equalish(a,b),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
less(a,b),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.60 % Computer : n006.cluster.edu
% 0.12/10.60 % Model : x86_64 x86_64
% 0.12/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.60 % Memory : 8046.5625MB
% 0.12/10.60 % OS : Linux 6.8.0-71-generic
% 0.12/10.60 % CPULimit : 300
% 0.12/10.60 % WCLimit : 300
% 0.12/10.60 % DateTime : Sat Sep 26 01:54:36 UTC 2026
% 0.12/10.60 % CPUTime :
% 0.12/10.60 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.15/12.45 % SZS status Unsatisfiable for theBenchmark.p
% 13.15/12.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------