TSTP Solution File: ANA003-4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA003-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 : Thu Jul 14 19:14:23 EDT 2022
% Result : Unsatisfiable 37.30s 37.47s
% Output : CNFRefutation 37.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 50 ( 4 unt; 31 nHn; 28 RR)
% Number of literals : 121 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(minimum3,axiom,
( ~ less_or_equal(Z,minimum(X,Y))
| less_or_equal(Z,X) ) ).
cnf(minimum7,axiom,
( ~ less_or_equal(Z,minimum(X,Y))
| less_or_equal(Z,Y) ) ).
cnf(minimum9,axiom,
( less_or_equal(X,n0)
| less_or_equal(Y,n0)
| ~ less_or_equal(minimum(X,Y),n0) ) ).
cnf(less_or_equal_sum_of_halves,axiom,
( ~ less_or_equal(X,half(Z))
| ~ less_or_equal(Y,half(Z))
| less_or_equal(add(X,Y),Z) ) ).
cnf(zero_and_half,axiom,
( less_or_equal(X,n0)
| ~ less_or_equal(half(X),n0) ) ).
cnf(clause_1,hypothesis,
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(delta_1(Epsilon),n0) ) ).
cnf(clause_2,hypothesis,
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(delta_2(Epsilon),n0) ) ).
cnf(clause_3,hypothesis,
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_1(Epsilon))
| less_or_equal(absolute(add(f(Z),negate(f(a_real_number)))),Epsilon) ) ).
cnf(clause_4,hypothesis,
( less_or_equal(Epsilon,n0)
| ~ less_or_equal(absolute(add(Z,negate(a_real_number))),delta_2(Epsilon))
| less_or_equal(absolute(add(g(Z),negate(g(a_real_number)))),Epsilon) ) ).
cnf(clause_5,hypothesis,
~ less_or_equal(epsilon_0,n0) ).
cnf(clause_6,hypothesis,
( less_or_equal(Delta,n0)
| less_or_equal(absolute(add(xs(Delta),negate(a_real_number))),Delta) ) ).
cnf(clause_7_2,negated_conjecture,
( less_or_equal(Delta,n0)
| ~ less_or_equal(add(absolute(add(f(xs(Delta)),negate(f(a_real_number)))),absolute(add(g(xs(Delta)),negate(g(a_real_number))))),epsilon_0) ) ).
cnf(refute_0_0,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(subst,[],[zero_and_half:[bind(X,$fot(epsilon_0))]]) ).
cnf(refute_0_1,plain,
( ~ less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(subst,[],[clause_1:[bind(Epsilon,$fot(half(epsilon_0)))]]) ).
cnf(refute_0_2,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(subst,[],[clause_2:[bind(Epsilon,$fot(half(epsilon_0)))]]) ).
cnf(refute_0_3,plain,
( ~ less_or_equal(minimum(X_2850,delta_1(half(epsilon_0))),n0)
| less_or_equal(X_2850,n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(subst,[],[minimum9:[bind(X,$fot(X_2850)),bind(Y,$fot(delta_1(half(epsilon_0))))]]) ).
cnf(refute_0_4,plain,
( ~ less_or_equal(minimum(delta_2(half(epsilon_0)),minimum(X_2849,delta_1(half(epsilon_0)))),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(minimum(X_2849,delta_1(half(epsilon_0))),n0) ),
inference(subst,[],[minimum9:[bind(X,$fot(delta_2(half(epsilon_0)))),bind(Y,$fot(minimum(X_2849,delta_1(half(epsilon_0)))))]]) ).
cnf(refute_0_5,plain,
( ~ less_or_equal(add(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))))),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))),n0) ),
inference(subst,[],[clause_7_2:[bind(Delta,$fot(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0))))))]]) ).
cnf(refute_0_6,plain,
( ~ less_or_equal(X,half(Z))
| ~ less_or_equal(absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number)))),half(Z))
| less_or_equal(add(X,absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number))))),Z) ),
inference(subst,[],[less_or_equal_sum_of_halves:[bind(Y,$fot(absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number))))))]]) ).
cnf(refute_0_7,plain,
( less_or_equal(absolute(add(xs(minimum(X_8,X_9)),negate(a_real_number))),minimum(X_8,X_9))
| less_or_equal(minimum(X_8,X_9),n0) ),
inference(subst,[],[clause_6:[bind(Delta,$fot(minimum(X_8,X_9)))]]) ).
cnf(refute_0_8,plain,
( ~ less_or_equal(absolute(add(xs(minimum(X_8,X_9)),negate(a_real_number))),minimum(X_8,X_9))
| less_or_equal(absolute(add(xs(minimum(X_8,X_9)),negate(a_real_number))),X_8) ),
inference(subst,[],[minimum3:[bind(X,$fot(X_8)),bind(Y,$fot(X_9)),bind(Z,$fot(absolute(add(xs(minimum(X_8,X_9)),negate(a_real_number)))))]]) ).
cnf(refute_0_9,plain,
( less_or_equal(absolute(add(xs(minimum(X_8,X_9)),negate(a_real_number))),X_8)
| less_or_equal(minimum(X_8,X_9),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(xs(minimum(X_8,X_9)),negate(a_real_number))),minimum(X_8,X_9)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( less_or_equal(absolute(add(xs(minimum(delta_2(X_35),X_9)),negate(a_real_number))),delta_2(X_35))
| less_or_equal(minimum(delta_2(X_35),X_9),n0) ),
inference(subst,[],[refute_0_9:[bind(X_8,$fot(delta_2(X_35)))]]) ).
cnf(refute_0_11,plain,
( ~ less_or_equal(absolute(add(xs(minimum(delta_2(X_35),X_9)),negate(a_real_number))),delta_2(X_35))
| less_or_equal(X_35,n0)
| less_or_equal(absolute(add(g(xs(minimum(delta_2(X_35),X_9))),negate(g(a_real_number)))),X_35) ),
inference(subst,[],[clause_4:[bind(Epsilon,$fot(X_35)),bind(Z,$fot(xs(minimum(delta_2(X_35),X_9))))]]) ).
cnf(refute_0_12,plain,
( less_or_equal(X_35,n0)
| less_or_equal(absolute(add(g(xs(minimum(delta_2(X_35),X_9))),negate(g(a_real_number)))),X_35)
| less_or_equal(minimum(delta_2(X_35),X_9),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(xs(minimum(delta_2(X_35),X_9)),negate(a_real_number))),delta_2(X_35)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( less_or_equal(absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number)))),half(Z))
| less_or_equal(half(Z),n0)
| less_or_equal(minimum(delta_2(half(Z)),X_41),n0) ),
inference(subst,[],[refute_0_12:[bind(X_35,$fot(half(Z))),bind(X_9,$fot(X_41))]]) ).
cnf(refute_0_14,plain,
( ~ less_or_equal(X,half(Z))
| less_or_equal(add(X,absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number))))),Z)
| less_or_equal(half(Z),n0)
| less_or_equal(minimum(delta_2(half(Z)),X_41),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number)))),half(Z)) )],[refute_0_13,refute_0_6]) ).
cnf(refute_0_15,plain,
( ~ less_or_equal(absolute(add(f(xs(minimum(X_327,minimum(X_326,delta_1(half(Z)))))),negate(f(a_real_number)))),half(Z))
| less_or_equal(add(absolute(add(f(xs(minimum(X_327,minimum(X_326,delta_1(half(Z)))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number))))),Z)
| less_or_equal(half(Z),n0)
| less_or_equal(minimum(delta_2(half(Z)),X_41),n0) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(absolute(add(f(xs(minimum(X_327,minimum(X_326,delta_1(half(Z)))))),negate(f(a_real_number))))))]]) ).
cnf(refute_0_16,plain,
( ~ less_or_equal(absolute(add(xs(minimum(X_44,minimum(X_42,delta_1(Epsilon)))),negate(a_real_number))),delta_1(Epsilon))
| less_or_equal(Epsilon,n0)
| less_or_equal(absolute(add(f(xs(minimum(X_44,minimum(X_42,delta_1(Epsilon))))),negate(f(a_real_number)))),Epsilon) ),
inference(subst,[],[clause_3:[bind(Z,$fot(xs(minimum(X_44,minimum(X_42,delta_1(Epsilon))))))]]) ).
cnf(refute_0_17,plain,
( ~ less_or_equal(absolute(add(xs(minimum(X_22,minimum(X,Y))),negate(a_real_number))),minimum(X,Y))
| less_or_equal(absolute(add(xs(minimum(X_22,minimum(X,Y))),negate(a_real_number))),Y) ),
inference(subst,[],[minimum7:[bind(Z,$fot(absolute(add(xs(minimum(X_22,minimum(X,Y))),negate(a_real_number)))))]]) ).
cnf(refute_0_18,plain,
( less_or_equal(absolute(add(xs(minimum(X_11,X_12)),negate(a_real_number))),minimum(X_11,X_12))
| less_or_equal(minimum(X_11,X_12),n0) ),
inference(subst,[],[clause_6:[bind(Delta,$fot(minimum(X_11,X_12)))]]) ).
cnf(refute_0_19,plain,
( ~ less_or_equal(absolute(add(xs(minimum(X_11,X_12)),negate(a_real_number))),minimum(X_11,X_12))
| less_or_equal(absolute(add(xs(minimum(X_11,X_12)),negate(a_real_number))),X_12) ),
inference(subst,[],[minimum7:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(absolute(add(xs(minimum(X_11,X_12)),negate(a_real_number)))))]]) ).
cnf(refute_0_20,plain,
( less_or_equal(absolute(add(xs(minimum(X_11,X_12)),negate(a_real_number))),X_12)
| less_or_equal(minimum(X_11,X_12),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(xs(minimum(X_11,X_12)),negate(a_real_number))),minimum(X_11,X_12)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( less_or_equal(absolute(add(xs(minimum(X_22,minimum(X,Y))),negate(a_real_number))),minimum(X,Y))
| less_or_equal(minimum(X_22,minimum(X,Y)),n0) ),
inference(subst,[],[refute_0_20:[bind(X_11,$fot(X_22)),bind(X_12,$fot(minimum(X,Y)))]]) ).
cnf(refute_0_22,plain,
( less_or_equal(absolute(add(xs(minimum(X_22,minimum(X,Y))),negate(a_real_number))),Y)
| less_or_equal(minimum(X_22,minimum(X,Y)),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(xs(minimum(X_22,minimum(X,Y))),negate(a_real_number))),minimum(X,Y)) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
( less_or_equal(absolute(add(xs(minimum(X_44,minimum(X_42,delta_1(Epsilon)))),negate(a_real_number))),delta_1(Epsilon))
| less_or_equal(minimum(X_44,minimum(X_42,delta_1(Epsilon))),n0) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_42)),bind(Y,$fot(delta_1(Epsilon))),bind(X_22,$fot(X_44))]]) ).
cnf(refute_0_24,plain,
( less_or_equal(Epsilon,n0)
| less_or_equal(absolute(add(f(xs(minimum(X_44,minimum(X_42,delta_1(Epsilon))))),negate(f(a_real_number)))),Epsilon)
| less_or_equal(minimum(X_44,minimum(X_42,delta_1(Epsilon))),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(xs(minimum(X_44,minimum(X_42,delta_1(Epsilon)))),negate(a_real_number))),delta_1(Epsilon)) )],[refute_0_23,refute_0_16]) ).
cnf(refute_0_25,plain,
( less_or_equal(absolute(add(f(xs(minimum(X_327,minimum(X_326,delta_1(half(Z)))))),negate(f(a_real_number)))),half(Z))
| less_or_equal(half(Z),n0)
| less_or_equal(minimum(X_327,minimum(X_326,delta_1(half(Z)))),n0) ),
inference(subst,[],[refute_0_24:[bind(Epsilon,$fot(half(Z))),bind(X_42,$fot(X_326)),bind(X_44,$fot(X_327))]]) ).
cnf(refute_0_26,plain,
( less_or_equal(add(absolute(add(f(xs(minimum(X_327,minimum(X_326,delta_1(half(Z)))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(Z)),X_41))),negate(g(a_real_number))))),Z)
| less_or_equal(half(Z),n0)
| less_or_equal(minimum(X_327,minimum(X_326,delta_1(half(Z)))),n0)
| less_or_equal(minimum(delta_2(half(Z)),X_41),n0) ),
inference(resolve,[$cnf( less_or_equal(absolute(add(f(xs(minimum(X_327,minimum(X_326,delta_1(half(Z)))))),negate(f(a_real_number)))),half(Z)) )],[refute_0_25,refute_0_15]) ).
cnf(refute_0_27,plain,
( less_or_equal(add(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))))),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))),n0) ),
inference(subst,[],[refute_0_26:[bind(Z,$fot(epsilon_0)),bind(X_326,$fot(X_2846)),bind(X_327,$fot(delta_2(half(epsilon_0)))),bind(X_41,$fot(minimum(X_2846,delta_1(half(epsilon_0)))))]]) ).
cnf(refute_0_28,plain,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))),n0) ),
inference(resolve,[$cnf( less_or_equal(add(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),minimum(X_2846,delta_1(half(epsilon_0)))))),negate(g(a_real_number))))),epsilon_0) )],[refute_0_27,refute_0_5]) ).
cnf(refute_0_29,plain,
( less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),minimum(X_2849,delta_1(half(epsilon_0)))),n0) ),
inference(subst,[],[refute_0_28:[bind(X_2846,$fot(X_2849))]]) ).
cnf(refute_0_30,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(X_2849,delta_1(half(epsilon_0))),n0) ),
inference(resolve,[$cnf( less_or_equal(minimum(delta_2(half(epsilon_0)),minimum(X_2849,delta_1(half(epsilon_0)))),n0) )],[refute_0_29,refute_0_4]) ).
cnf(refute_0_31,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0)
| less_or_equal(minimum(X_2850,delta_1(half(epsilon_0))),n0) ),
inference(subst,[],[refute_0_30:[bind(X_2849,$fot(X_2850))]]) ).
cnf(refute_0_32,plain,
( less_or_equal(X_2850,n0)
| less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(resolve,[$cnf( less_or_equal(minimum(X_2850,delta_1(half(epsilon_0))),n0) )],[refute_0_31,refute_0_3]) ).
cnf(refute_0_33,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(subst,[],[refute_0_32:[bind(X_2850,$fot(half(epsilon_0)))]]) ).
cnf(refute_0_34,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(resolve,[$cnf( less_or_equal(delta_2(half(epsilon_0)),n0) )],[refute_0_33,refute_0_2]) ).
cnf(refute_0_35,plain,
less_or_equal(half(epsilon_0),n0),
inference(resolve,[$cnf( less_or_equal(delta_1(half(epsilon_0)),n0) )],[refute_0_34,refute_0_1]) ).
cnf(refute_0_36,plain,
less_or_equal(epsilon_0,n0),
inference(resolve,[$cnf( less_or_equal(half(epsilon_0),n0) )],[refute_0_35,refute_0_0]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( less_or_equal(epsilon_0,n0) )],[refute_0_36,clause_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 03:11:15 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 37.30/37.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.30/37.47
% 37.30/37.47 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.30/37.48
%------------------------------------------------------------------------------