TSTP Solution File: ANA021-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA021-2 : TPTP v8.1.0. Released v3.2.0.
% 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 19:14:38 EDT 2022
% Result : Unsatisfiable 0.15s 0.37s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 7 unt; 13 nHn; 15 RR)
% Number of literals : 54 ( 34 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_NatBin_OSuc__pred_H_0,axiom,
( ~ c_less(c_0,V_x,tc_nat)
| V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( c_less(c_0,V_n,tc_nat)
| V_n = c_0 ) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a) ).
cnf(cls_conjecture_3,negated_conjecture,
v_x != c_0 ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ).
cnf(refute_0_0,plain,
c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a),
inference(subst,[],[cls_conjecture_2:[bind(V_U,$fot(c_minus(X_3,c_1,tc_nat)))]]) ).
cnf(refute_0_1,plain,
( X_2 = c_0
| c_less(c_0,X_2,tc_nat) ),
inference(subst,[],[cls_Nat_Onot__gr0_0:[bind(V_n,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( ~ c_less(c_0,X_2,tc_nat)
| X_2 = c_Suc(c_minus(X_2,c_1,tc_nat)) ),
inference(subst,[],[cls_NatBin_OSuc__pred_H_0:[bind(V_x,$fot(X_2))]]) ).
cnf(refute_0_3,plain,
( X_2 = c_0
| X_2 = c_Suc(c_minus(X_2,c_1,tc_nat)) ),
inference(resolve,[$cnf( c_less(c_0,X_2,tc_nat) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( X_3 = c_0
| X_3 = c_Suc(c_minus(X_3,c_1,tc_nat)) ),
inference(subst,[],[refute_0_3:[bind(X_2,$fot(X_3))]]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( X_3 != c_Suc(c_minus(X_3,c_1,tc_nat))
| c_Suc(c_minus(X_3,c_1,tc_nat)) = X_3 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_3)),bind(Y,$fot(c_Suc(c_minus(X_3,c_1,tc_nat))))]]) ).
cnf(refute_0_9,plain,
( X_3 = c_0
| c_Suc(c_minus(X_3,c_1,tc_nat)) = X_3 ),
inference(resolve,[$cnf( $equal(X_3,c_Suc(c_minus(X_3,c_1,tc_nat))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( c_Suc(c_minus(X_3,c_1,tc_nat)) != X_3
| ~ c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(X_3),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a) ),[0,0,0],$fot(X_3)]]) ).
cnf(refute_0_11,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a)
| X_3 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_3),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_Suc(c_minus(X_3,c_1,tc_nat)),X_3) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( X_3 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_3),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_3,c_1,tc_nat))),t_a),t_a),t_a) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
( X_4 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_4,c_1,tc_nat))),t_a),t_a),t_a) ),
inference(subst,[],[refute_0_12:[bind(X_3,$fot(X_4))]]) ).
cnf(refute_0_14,plain,
( X_4 = c_0
| X_4 = c_Suc(c_minus(X_4,c_1,tc_nat)) ),
inference(subst,[],[refute_0_3:[bind(X_2,$fot(X_4))]]) ).
cnf(refute_0_15,plain,
( X_4 != c_Suc(c_minus(X_4,c_1,tc_nat))
| c_Suc(c_minus(X_4,c_1,tc_nat)) = X_4 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(X_4)),bind(Y,$fot(c_Suc(c_minus(X_4,c_1,tc_nat))))]]) ).
cnf(refute_0_16,plain,
( X_4 = c_0
| c_Suc(c_minus(X_4,c_1,tc_nat)) = X_4 ),
inference(resolve,[$cnf( $equal(X_4,c_Suc(c_minus(X_4,c_1,tc_nat))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( c_Suc(c_minus(X_4,c_1,tc_nat)) != X_4
| ~ c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_4,c_1,tc_nat))),t_a),t_a),t_a)
| c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(X_4),t_a),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_4,c_1,tc_nat))),t_a),t_a),t_a) ),[1,1,0,0],$fot(X_4)]]) ).
cnf(refute_0_18,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_4,c_1,tc_nat))),t_a),t_a),t_a)
| X_4 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(X_4),t_a),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_Suc(c_minus(X_4,c_1,tc_nat)),X_4) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( X_4 = c_0
| c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(X_4),t_a),t_a),t_a) ),
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(X_4),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(c_minus(X_4,c_1,tc_nat))),t_a),t_a),t_a) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
( v_x = c_0
| c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) ),
inference(subst,[],[refute_0_19:[bind(X_4,$fot(v_x))]]) ).
cnf(refute_0_21,plain,
v_x = c_0,
inference(resolve,[$cnf( c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a) )],[refute_0_20,cls_conjecture_4]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( $equal(v_x,c_0) )],[refute_0_21,cls_conjecture_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ANA021-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jul 8 04:29:15 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37
% 0.15/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.38
%------------------------------------------------------------------------------