%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:24:10 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 8 unt; 6 nHn; 24 RR)
% Number of literals : 48 ( 0 equ; 19 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ) ).
cnf(smaller_number,axiom,
( ~ equalish(add(successor(A),B),C)
| less(B,C) ) ).
cnf(less_lemma,axiom,
( ~ less(A,B)
| equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B) ) ).
cnf(divides_only_less_or_equal,axiom,
( ~ divides(A,B)
| less(A,B)
| equalish(A,B) ) ).
cnf(transitivity,axiom,
( ~ equalish(A,B)
| ~ equalish(C,A)
| equalish(C,B) ) ).
cnf(a_less_than_b,hypothesis,
less(a,b) ).
cnf(b_divides_d,hypothesis,
divides(b,d) ).
cnf(prove_a_less_than_d,negated_conjecture,
~ less(a,d) ).
cnf(refute_0_0,plain,
( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d)
| less(a,d) ),
inference(subst,[],[smaller_number:[bind(A,$fot(predecessor_of_1st_minus_2nd(b,a))),bind(B,$fot(a)),bind(C,$fot(d))]]) ).
cnf(refute_0_1,plain,
( ~ less(a,b)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b) ),
inference(subst,[],[less_lemma:[bind(A,$fot(a)),bind(B,$fot(b))]]) ).
cnf(refute_0_2,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b),
inference(resolve,[$cnf( less(a,b) )],[a_less_than_b,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ divides(b,d)
| equalish(b,d)
| less(b,d) ),
inference(subst,[],[divides_only_less_or_equal:[bind(A,$fot(b)),bind(B,$fot(d))]]) ).
cnf(refute_0_4,plain,
( equalish(b,d)
| less(b,d) ),
inference(resolve,[$cnf( divides(b,d) )],[b_divides_d,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ less(X_13,b)
| ~ less(b,d)
| less(X_13,d) ),
inference(subst,[],[transitivity_of_less:[bind(A,$fot(b)),bind(B,$fot(d)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_6,plain,
( ~ less(X_13,b)
| equalish(b,d)
| less(X_13,d) ),
inference(resolve,[$cnf( less(b,d) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ less(a,b)
| equalish(b,d)
| less(a,d) ),
inference(subst,[],[refute_0_6:[bind(X_13,$fot(a))]]) ).
cnf(refute_0_8,plain,
( equalish(b,d)
| less(a,d) ),
inference(resolve,[$cnf( less(a,b) )],[a_less_than_b,refute_0_7]) ).
cnf(refute_0_9,plain,
equalish(b,d),
inference(resolve,[$cnf( less(a,d) )],[refute_0_8,prove_a_less_than_d]) ).
cnf(refute_0_10,plain,
( ~ equalish(X_18,b)
| ~ equalish(b,d)
| equalish(X_18,d) ),
inference(subst,[],[transitivity:[bind(A,$fot(b)),bind(B,$fot(d)),bind(C,$fot(X_18))]]) ).
cnf(refute_0_11,plain,
( ~ equalish(X_18,b)
| equalish(X_18,d) ),
inference(resolve,[$cnf( equalish(b,d) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d) ),
inference(subst,[],[refute_0_11:[bind(X_18,$fot(add(successor(predecessor_of_1st_minus_2nd(b,a)),a)))]]) ).
cnf(refute_0_13,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d),
inference(resolve,[$cnf( equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
less(a,d),
inference(resolve,[$cnf( equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( less(a,d) )],[refute_0_14,prove_a_less_than_d]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 00:12:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------