TSTP Solution File: ANA016-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ANA016-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 19:14:34 EDT 2022
% Result : Unsatisfiable 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 42 ( 14 unt; 10 nHn; 27 RR)
% Number of literals : 78 ( 55 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
v_c != c_0 ).
cnf(cls_conjecture_2,negated_conjecture,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a) ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_times(c_1,V_y,T_a) = V_y ) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ) ).
cnf(cls_Ring__and__Field_Oright__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ).
cnf(clsrel_Ring__and__Field_Ofield_12,axiom,
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ) ).
cnf(refute_0_0,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| class_OrderedGroup_Osemigroup__mult(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Ofield_21:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_1,plain,
( ~ class_Ring__and__Field_Oordered__field(t_a)
| class_Ring__and__Field_Ofield(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Oordered__field_0:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_2,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Oordered__field(t_a) )],[tfree_tcs,refute_0_1]) ).
cnf(refute_0_3,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Ofield(t_a) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| c_times(c_times(X_10,X_11,t_a),X_12,t_a) = c_times(X_10,c_times(X_11,X_12,t_a),t_a) ),
inference(subst,[],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_10)),bind(V_b,$fot(X_11)),bind(V_c,$fot(X_12))]]) ).
cnf(refute_0_5,plain,
c_times(c_times(X_10,X_11,t_a),X_12,t_a) = c_times(X_10,c_times(X_11,X_12,t_a),t_a),
inference(resolve,[$cnf( class_OrderedGroup_Osemigroup__mult(t_a) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
c_times(c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a),X_15,t_a) = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a),
inference(subst,[],[refute_0_5:[bind(X_10,$fot(X_13)),bind(X_11,$fot(c_HOL_Oinverse(X_13,t_a))),bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_7,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| X_7 = c_0
| c_times(X_7,c_HOL_Oinverse(X_7,t_a),t_a) = c_1 ),
inference(subst,[],[cls_Ring__and__Field_Oright__inverse_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_7))]]) ).
cnf(refute_0_8,plain,
( X_7 = c_0
| c_times(X_7,c_HOL_Oinverse(X_7,t_a),t_a) = c_1 ),
inference(resolve,[$cnf( class_Ring__and__Field_Ofield(t_a) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( X_13 = c_0
| c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a) = c_1 ),
inference(subst,[],[refute_0_8:[bind(X_7,$fot(X_13))]]) ).
cnf(refute_0_10,plain,
( c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a) != c_1
| c_times(c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a),X_15,t_a) != c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)
| c_times(c_1,X_15,t_a) = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_times(c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a),X_15,t_a),c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)) ),[0,0],$fot(c_1)]]) ).
cnf(refute_0_11,plain,
( c_times(c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a),X_15,t_a) != c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)
| X_13 = c_0
| c_times(c_1,X_15,t_a) = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a),c_1) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( X_13 = c_0
| c_times(c_1,X_15,t_a) = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_times(X_13,c_HOL_Oinverse(X_13,t_a),t_a),X_15,t_a),c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ class_Ring__and__Field_Ofield(t_a)
| class_OrderedGroup_Omonoid__mult(t_a) ),
inference(subst,[],[clsrel_Ring__and__Field_Ofield_12:[bind(T,$fot(t_a))]]) ).
cnf(refute_0_14,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolve,[$cnf( class_Ring__and__Field_Ofield(t_a) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ class_OrderedGroup_Omonoid__mult(t_a)
| c_times(c_1,X_4,t_a) = X_4 ),
inference(subst,[],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0:[bind(T_a,$fot(t_a)),bind(V_y,$fot(X_4))]]) ).
cnf(refute_0_16,plain,
c_times(c_1,X_4,t_a) = X_4,
inference(resolve,[$cnf( class_OrderedGroup_Omonoid__mult(t_a) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
c_times(c_1,X_15,t_a) = X_15,
inference(subst,[],[refute_0_16:[bind(X_4,$fot(X_15))]]) ).
cnf(refute_0_18,plain,
( c_times(c_1,X_15,t_a) != X_15
| c_times(c_1,X_15,t_a) != c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)
| X_15 = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_times(c_1,X_15,t_a),c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)) ),[0],$fot(X_15)]]) ).
cnf(refute_0_19,plain,
( c_times(c_1,X_15,t_a) != c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)
| X_15 = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_1,X_15,t_a),X_15) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( X_13 = c_0
| X_15 = c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(c_1,X_15,t_a),c_times(X_13,c_times(c_HOL_Oinverse(X_13,t_a),X_15,t_a),t_a)) )],[refute_0_12,refute_0_19]) ).
cnf(refute_0_21,plain,
( v_c = c_0
| v_g(v_x) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ),
inference(subst,[],[refute_0_20:[bind(X_13,$fot(v_c)),bind(X_15,$fot(v_g(v_x)))]]) ).
cnf(refute_0_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)
| c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) = v_g(v_x) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(v_g(v_x))),bind(Y,$fot(c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)))]]) ).
cnf(refute_0_26,plain,
( c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) = v_g(v_x)
| v_c = c_0 ),
inference(resolve,[$cnf( $equal(v_g(v_x),c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) != v_g(v_x)
| v_g(v_x) != v_g(v_x)
| v_g(v_x) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ),
introduced(tautology,[equality,[$cnf( ~ $equal(v_g(v_x),c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)) ),[1],$fot(v_g(v_x))]]) ).
cnf(refute_0_28,plain,
( v_g(v_x) != v_g(v_x)
| v_c = c_0
| v_g(v_x) = c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) ),
inference(resolve,[$cnf( $equal(c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),v_g(v_x)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( v_g(v_x) != v_g(v_x)
| v_c = c_0 ),
inference(resolve,[$cnf( $equal(v_g(v_x),c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)) )],[refute_0_28,cls_conjecture_2]) ).
cnf(refute_0_30,plain,
v_g(v_x) = v_g(v_x),
introduced(tautology,[refl,[$fot(v_g(v_x))]]) ).
cnf(refute_0_31,plain,
v_c = c_0,
inference(resolve,[$cnf( $equal(v_g(v_x),v_g(v_x)) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(v_c,c_0) )],[refute_0_31,cls_conjecture_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ANA016-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 02:45:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------