TSTP Solution File: NUM027-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 12:24:12 EDT 2022
% Result : Unsatisfiable 0.47s 0.65s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 10 unt; 9 nHn; 20 RR)
% Number of literals : 53 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 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 : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ) ).
cnf(equality_preserved_over_times,axiom,
( ~ equalish(A,B)
| equalish(multiply(A,C),multiply(B,C)) ) ).
cnf(not_less_and_equal,axiom,
( ~ less(A,B)
| ~ equalish(A,B) ) ).
cnf(numbers_either_less_or_equal,axiom,
( less(A,B)
| equalish(B,A)
| less(B,A) ) ).
cnf(number_not_less_than_itself,axiom,
~ less(A,A) ).
cnf(multiply_lemma,axiom,
( ~ less(A,B)
| equalish(C,n0)
| less(multiply(A,C),multiply(B,C)) ) ).
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(refute_0_0,plain,
( ~ equalish(multiply(b,c),multiply(a,c))
| ~ less(multiply(b,c),multiply(a,c)) ),
inference(subst,[],[not_less_and_equal:[bind(A,$fot(multiply(b,c))),bind(B,$fot(multiply(a,c)))]]) ).
cnf(refute_0_1,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolve,[$cnf( less(multiply(b,c),multiply(a,c)) )],[b_times_c_less_than_a_times_c,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ equalish(b,a)
| equalish(multiply(b,C),multiply(a,C)) ),
inference(subst,[],[equality_preserved_over_times:[bind(A,$fot(b)),bind(B,$fot(a))]]) ).
cnf(refute_0_3,plain,
( ~ less(X_297,multiply(b,c))
| ~ less(multiply(b,c),multiply(a,c))
| less(X_297,multiply(a,c)) ),
inference(subst,[],[transitivity_of_less:[bind(A,$fot(multiply(b,c))),bind(B,$fot(multiply(a,c))),bind(C,$fot(X_297))]]) ).
cnf(refute_0_4,plain,
( ~ less(X_297,multiply(b,c))
| less(X_297,multiply(a,c)) ),
inference(resolve,[$cnf( less(multiply(b,c),multiply(a,c)) )],[b_times_c_less_than_a_times_c,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ less(multiply(a,c),multiply(b,c))
| less(multiply(a,c),multiply(a,c)) ),
inference(subst,[],[refute_0_4:[bind(X_297,$fot(multiply(a,c)))]]) ).
cnf(refute_0_6,plain,
( equalish(b,a)
| less(a,b)
| less(b,a) ),
inference(subst,[],[numbers_either_less_or_equal:[bind(A,$fot(a)),bind(B,$fot(b))]]) ).
cnf(refute_0_7,plain,
( equalish(b,a)
| less(a,b) ),
inference(resolve,[$cnf( less(b,a) )],[refute_0_6,b_not_less_than_a]) ).
cnf(refute_0_8,plain,
( ~ less(a,b)
| equalish(X_590,n0)
| less(multiply(a,X_590),multiply(b,X_590)) ),
inference(subst,[],[multiply_lemma:[bind(A,$fot(a)),bind(B,$fot(b)),bind(C,$fot(X_590))]]) ).
cnf(refute_0_9,plain,
( equalish(X_590,n0)
| equalish(b,a)
| less(multiply(a,X_590),multiply(b,X_590)) ),
inference(resolve,[$cnf( less(a,b) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( equalish(b,a)
| equalish(c,n0)
| less(multiply(a,c),multiply(b,c)) ),
inference(subst,[],[refute_0_9:[bind(X_590,$fot(c))]]) ).
cnf(refute_0_11,plain,
( equalish(b,a)
| equalish(c,n0)
| less(multiply(a,c),multiply(a,c)) ),
inference(resolve,[$cnf( less(multiply(a,c),multiply(b,c)) )],[refute_0_10,refute_0_5]) ).
cnf(refute_0_12,plain,
( equalish(b,a)
| less(multiply(a,c),multiply(a,c)) ),
inference(resolve,[$cnf( equalish(c,n0) )],[refute_0_11,prove_c_is_0]) ).
cnf(refute_0_13,plain,
~ less(multiply(a,c),multiply(a,c)),
inference(subst,[],[number_not_less_than_itself:[bind(A,$fot(multiply(a,c)))]]) ).
cnf(refute_0_14,plain,
equalish(b,a),
inference(resolve,[$cnf( less(multiply(a,c),multiply(a,c)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
equalish(multiply(b,C),multiply(a,C)),
inference(resolve,[$cnf( equalish(b,a) )],[refute_0_14,refute_0_2]) ).
cnf(refute_0_16,plain,
equalish(multiply(b,c),multiply(a,c)),
inference(subst,[],[refute_0_15:[bind(C,$fot(c))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( equalish(multiply(b,c),multiply(a,c)) )],[refute_0_16,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.11/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Wed Jul 6 13:45:14 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.65
% 0.47/0.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.47/0.65
%------------------------------------------------------------------------------