TSTP Solution File: ANA027-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA027-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n010.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 : 300s
% DateTime : Tue Aug 22 10:32:50 EDT 2023
% Result : Unsatisfiable 2.97s 1.74s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 62 ( 23 unt; 15 typ; 0 def)
% Number of atoms : 82 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 42 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 49 (; 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__abs > class_OrderedGroup_Ocomm__monoid__add > class_LOrder_Ojoin__semilorder > c_plus > c_minus > #nlpp > v_k > v_g > v_f > v_x > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_0,type,
c_0: $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_plus,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(class_LOrder_Ojoin__semilorder,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
tff(v_g,type,
v_g: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(v_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(v_k,type,
v_k: $i > $i ).
tff(f_30,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_87,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [T] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file(unknown,unknown) ).
tff(f_82,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [T_a,V_y] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_29,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file(unknown,unknown) ).
tff(f_26,axiom,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file(unknown,unknown) ).
tff(f_43,axiom,
! [T_a,V_a,V_c,V_b] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [T] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_LOrder_Ojoin__semilorder(T) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [T] :
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_27,axiom,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file(unknown,unknown) ).
tff(f_62,axiom,
! [T_a,V_y,V_z,V_x] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| c_lessequals(V_x,V_z,T_a) ),
file(unknown,unknown) ).
tff(c_8,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_27,plain,
! [T_20] :
( class_OrderedGroup_Olordered__ab__group__abs(T_20)
| ~ class_Ring__and__Field_Oordered__idom(T_20) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_31,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_8,c_27]) ).
tff(c_20,plain,
! [T_16] :
( class_OrderedGroup_Opordered__ab__group__add(T_16)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_16) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_32,plain,
! [T_21] :
( class_OrderedGroup_Ocomm__monoid__add(T_21)
| ~ class_Ring__and__Field_Oordered__idom(T_21) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_36,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolution,[status(thm)],[c_8,c_32]) ).
tff(c_44,plain,
! [V_y_25,T_a_26] :
( ( c_plus(c_0,V_y_25,T_a_26) = V_y_25 )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_26) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_47,plain,
! [V_y_25] : ( c_plus(c_0,V_y_25,t_b) = V_y_25 ),
inference(resolution,[status(thm)],[c_36,c_44]) ).
tff(c_81,plain,
! [V_a_36,V_c_37,V_b_38,T_a_39] :
( c_lessequals(V_a_36,c_minus(V_c_37,V_b_38,T_a_39),T_a_39)
| ~ c_lessequals(c_plus(V_a_36,V_b_38,T_a_39),V_c_37,T_a_39)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_39) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_87,plain,
! [V_c_37,V_y_25] :
( c_lessequals(c_0,c_minus(V_c_37,V_y_25,t_b),t_b)
| ~ c_lessequals(V_y_25,V_c_37,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_47,c_81]) ).
tff(c_90,plain,
~ class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(splitLeft,[status(thm)],[c_87]) ).
tff(c_93,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_20,c_90]) ).
tff(c_97,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_31,c_93]) ).
tff(c_100,plain,
! [V_c_41,V_y_42] :
( c_lessequals(c_0,c_minus(V_c_41,V_y_42,t_b),t_b)
| ~ c_lessequals(V_y_42,V_c_41,t_b) ),
inference(splitRight,[status(thm)],[c_87]) ).
tff(c_6,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_109,plain,
~ c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[status(thm)],[c_100,c_6]) ).
tff(c_2,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_99,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(splitRight,[status(thm)],[c_87]) ).
tff(c_64,plain,
! [V_a_32,V_b_33,T_a_34,V_c_35] :
( c_lessequals(c_plus(V_a_32,V_b_33,T_a_34),V_c_35,T_a_34)
| ~ c_lessequals(V_a_32,c_minus(V_c_35,V_b_33,T_a_34),T_a_34)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_34) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_69,plain,
! [V_y_25,V_c_35] :
( c_lessequals(V_y_25,V_c_35,t_b)
| ~ c_lessequals(c_0,c_minus(V_c_35,V_y_25,t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_47,c_64]) ).
tff(c_115,plain,
! [V_y_44,V_c_45] :
( c_lessequals(V_y_44,V_c_45,t_b)
| ~ c_lessequals(c_0,c_minus(V_c_45,V_y_44,t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_99,c_69]) ).
tff(c_123,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(resolution,[status(thm)],[c_2,c_115]) ).
tff(c_38,plain,
! [T_23] :
( class_LOrder_Ojoin__semilorder(T_23)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_23) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_42,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[c_31,c_38]) ).
tff(c_18,plain,
! [T_15] :
( class_Orderings_Oorder(T_15)
| ~ class_LOrder_Ojoin__semilorder(T_15) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_57,plain,
! [V_x_28,V_z_29,T_a_30,V_y_31] :
( c_lessequals(V_x_28,V_z_29,T_a_30)
| ~ c_lessequals(V_x_28,V_y_31,T_a_30)
| ~ c_lessequals(V_y_31,V_z_29,T_a_30)
| ~ class_Orderings_Oorder(T_a_30) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_63,plain,
! [V_z_29] :
( c_lessequals(v_g(v_x),V_z_29,t_b)
| ~ c_lessequals(v_k(v_x),V_z_29,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_4,c_57]) ).
tff(c_71,plain,
~ class_Orderings_Oorder(t_b),
inference(splitLeft,[status(thm)],[c_63]) ).
tff(c_74,plain,
~ class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[c_18,c_71]) ).
tff(c_78,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42,c_74]) ).
tff(c_79,plain,
! [V_z_29] :
( c_lessequals(v_g(v_x),V_z_29,t_b)
| ~ c_lessequals(v_k(v_x),V_z_29,t_b) ),
inference(splitRight,[status(thm)],[c_63]) ).
tff(c_126,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[status(thm)],[c_123,c_79]) ).
tff(c_132,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_109,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA027-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n010.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 : 300
% 0.15/0.36 % DateTime : Thu Aug 3 15:20:29 EDT 2023
% 0.15/0.36 % CPUTime :
% 2.97/1.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.97/1.74
% 2.97/1.74 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.97/1.78
% 2.97/1.78 Inference rules
% 2.97/1.78 ----------------------
% 2.97/1.78 #Ref : 0
% 2.97/1.78 #Sup : 20
% 2.97/1.78 #Fact : 0
% 2.97/1.78 #Define : 0
% 2.97/1.78 #Split : 2
% 2.97/1.78 #Chain : 0
% 2.97/1.78 #Close : 0
% 2.97/1.78
% 2.97/1.78 Ordering : KBO
% 2.97/1.78
% 2.97/1.78 Simplification rules
% 2.97/1.78 ----------------------
% 2.97/1.78 #Subsume : 0
% 2.97/1.78 #Demod : 5
% 2.97/1.78 #Tautology : 4
% 2.97/1.78 #SimpNegUnit : 1
% 2.97/1.78 #BackRed : 0
% 2.97/1.78
% 2.97/1.78 #Partial instantiations: 0
% 2.97/1.78 #Strategies tried : 1
% 2.97/1.78
% 2.97/1.78 Timing (in seconds)
% 2.97/1.78 ----------------------
% 2.97/1.78 Preprocessing : 0.44
% 2.97/1.78 Parsing : 0.24
% 2.97/1.78 CNF conversion : 0.02
% 2.97/1.78 Main loop : 0.26
% 2.97/1.78 Inferencing : 0.11
% 2.97/1.78 Reduction : 0.07
% 2.97/1.78 Demodulation : 0.04
% 2.97/1.78 BG Simplification : 0.01
% 2.97/1.78 Subsumption : 0.05
% 2.97/1.78 Abstraction : 0.01
% 2.97/1.78 MUC search : 0.00
% 2.97/1.78 Cooper : 0.00
% 2.97/1.78 Total : 0.75
% 2.97/1.78 Index Insertion : 0.00
% 2.97/1.79 Index Deletion : 0.00
% 2.97/1.79 Index Matching : 0.00
% 2.97/1.79 BG Taut test : 0.00
%------------------------------------------------------------------------------