TSTP Solution File: ANA030-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA030-2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 20.42s 8.33s
% Output : CNFRefutation 20.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 35
% Syntax : Number of formulae : 72 ( 18 unt; 19 typ; 0 def)
% Number of atoms : 106 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 110 ( 57 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 16 >; 12 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 91 (; 91 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__abs > class_OrderedGroup_Oab__group__add > c_times > c_plus > c_minus > c_Orderings_Omax > c_uminus > c_HOL_Oabs > #nlpp > v_x > v_h > v_g > v_f > v_c > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(v_c,type,
v_c: $i ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(v_h,type,
v_h: $i > $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(c_0,type,
c_0: $i ).
tff(c_times,type,
c_times: ( $i * $i * $i ) > $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(c_plus,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(c_Orderings_Omax,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_uminus,type,
c_uminus: ( $i * $i ) > $i ).
tff(v_g,type,
v_g: $i > $i ).
tff(v_x,type,
v_x: $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(f_31,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_100,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_plus(V_a,V_b,T_a),T_a) = c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_44,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_b,T_a),T_a) = c_minus(V_a,V_b,T_a) ) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_minus(V_a,V_b,T_a),T_a) = c_minus(V_b,V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [T_a,V_y] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_uminus(c_uminus(V_y,T_a),T_a) = V_y ) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_minus(V_a,c_uminus(V_b,T_a),T_a) = c_plus(V_a,V_b,T_a) ) ),
file(unknown,unknown) ).
tff(f_105,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_90,axiom,
! [T] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file(unknown,unknown) ).
tff(f_95,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file(unknown,unknown) ).
tff(f_77,axiom,
! [T_b,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_b)
| c_lessequals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b) ),
file(unknown,unknown) ).
tff(f_39,axiom,
! [T_a,V_y] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ~ c_lessequals(c_0,V_y,T_a)
| ( c_HOL_Oabs(V_y,T_a) = V_y ) ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_85,axiom,
! [T_b,V_x,V_y,V_z] :
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| c_lessequals(V_x,V_z,T_b) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_plus(V_c,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [V_U] : ~ c_lessequals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(c_6,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_33,plain,
! [T_34] :
( class_OrderedGroup_Oab__group__add(T_34)
| ~ class_Ring__and__Field_Oordered__idom(T_34) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_37,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[status(thm)],[c_6,c_33]) ).
tff(c_158,plain,
! [V_a_68,T_a_69,V_b_70] :
( ( c_plus(c_uminus(V_a_68,T_a_69),c_uminus(V_b_70,T_a_69),T_a_69) = c_uminus(c_plus(V_a_68,V_b_70,T_a_69),T_a_69) )
| ~ class_OrderedGroup_Oab__group__add(T_a_69) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_10,plain,
! [V_a_6,V_b_7,T_a_5] :
( ( c_plus(V_a_6,c_uminus(V_b_7,T_a_5),T_a_5) = c_minus(V_a_6,V_b_7,T_a_5) )
| ~ class_OrderedGroup_Oab__group__add(T_a_5) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_231,plain,
! [V_a_79,T_a_80,V_b_81] :
( ( c_minus(c_uminus(V_a_79,T_a_80),V_b_81,T_a_80) = c_uminus(c_plus(V_a_79,V_b_81,T_a_80),T_a_80) )
| ~ class_OrderedGroup_Oab__group__add(T_a_80)
| ~ class_OrderedGroup_Oab__group__add(T_a_80) ),
inference(superposition,[status(thm),theory(equality)],[c_158,c_10]) ).
tff(c_18,plain,
! [V_a_19,V_b_20,T_a_18] :
( ( c_uminus(c_minus(V_a_19,V_b_20,T_a_18),T_a_18) = c_minus(V_b_20,V_a_19,T_a_18) )
| ~ class_OrderedGroup_Oab__group__add(T_a_18) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1218,plain,
! [V_a_143,V_b_144,T_a_145] :
( ( c_uminus(c_uminus(c_plus(V_a_143,V_b_144,T_a_145),T_a_145),T_a_145) = c_minus(V_b_144,c_uminus(V_a_143,T_a_145),T_a_145) )
| ~ class_OrderedGroup_Oab__group__add(T_a_145)
| ~ class_OrderedGroup_Oab__group__add(T_a_145)
| ~ class_OrderedGroup_Oab__group__add(T_a_145) ),
inference(superposition,[status(thm),theory(equality)],[c_231,c_18]) ).
tff(c_20,plain,
! [V_y_22,T_a_21] :
( ( c_uminus(c_uminus(V_y_22,T_a_21),T_a_21) = V_y_22 )
| ~ class_OrderedGroup_Oab__group__add(T_a_21) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_1315,plain,
! [V_b_146,V_a_147,T_a_148] :
( ( c_minus(V_b_146,c_uminus(V_a_147,T_a_148),T_a_148) = c_plus(V_a_147,V_b_146,T_a_148) )
| ~ class_OrderedGroup_Oab__group__add(T_a_148)
| ~ class_OrderedGroup_Oab__group__add(T_a_148)
| ~ class_OrderedGroup_Oab__group__add(T_a_148)
| ~ class_OrderedGroup_Oab__group__add(T_a_148) ),
inference(superposition,[status(thm),theory(equality)],[c_1218,c_20]) ).
tff(c_14,plain,
! [V_a_13,V_b_14,T_a_12] :
( ( c_minus(V_a_13,c_uminus(V_b_14,T_a_12),T_a_12) = c_plus(V_a_13,V_b_14,T_a_12) )
| ~ class_OrderedGroup_Oab__group__add(T_a_12) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1399,plain,
! [V_b_149,V_a_150,T_a_151] :
( ( c_plus(V_b_149,V_a_150,T_a_151) = c_plus(V_a_150,V_b_149,T_a_151) )
| ~ class_OrderedGroup_Oab__group__add(T_a_151)
| ~ class_OrderedGroup_Oab__group__add(T_a_151)
| ~ class_OrderedGroup_Oab__group__add(T_a_151)
| ~ class_OrderedGroup_Oab__group__add(T_a_151)
| ~ class_OrderedGroup_Oab__group__add(T_a_151) ),
inference(superposition,[status(thm),theory(equality)],[c_1315,c_14]) ).
tff(c_1401,plain,
! [V_b_149,V_a_150] :
( ( c_plus(V_b_149,V_a_150,t_b) = c_plus(V_a_150,V_b_149,t_b) )
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(resolution,[status(thm)],[c_37,c_1399]) ).
tff(c_1404,plain,
! [V_b_149,V_a_150] : ( c_plus(V_b_149,V_a_150,t_b) = c_plus(V_a_150,V_b_149,t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_37,c_1401]) ).
tff(c_44,plain,
! [T_37] :
( class_OrderedGroup_Olordered__ab__group__abs(T_37)
| ~ class_Ring__and__Field_Oordered__idom(T_37) ),
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_48,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_6,c_44]) ).
tff(c_26,plain,
! [T_30] :
( class_OrderedGroup_Opordered__ab__group__add(T_30)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_30) ),
inference(cnfTransformation,[status(thm)],[f_90]) ).
tff(c_38,plain,
! [T_35] :
( class_Orderings_Olinorder(T_35)
| ~ class_Ring__and__Field_Oordered__idom(T_35) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_42,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_6,c_38]) ).
tff(c_22,plain,
! [V_y_24,V_x_25,T_b_23] :
( c_lessequals(V_y_24,c_Orderings_Omax(V_x_25,V_y_24,T_b_23),T_b_23)
| ~ class_Orderings_Olinorder(T_b_23) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_67,plain,
! [V_y_43,T_a_44] :
( ( c_HOL_Oabs(V_y_43,T_a_44) = V_y_43 )
| ~ c_lessequals(c_0,V_y_43,T_a_44)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_44) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_72,plain,
! [V_x_25,T_b_23] :
( ( c_HOL_Oabs(c_Orderings_Omax(V_x_25,c_0,T_b_23),T_b_23) = c_Orderings_Omax(V_x_25,c_0,T_b_23) )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_b_23)
| ~ class_Orderings_Olinorder(T_b_23) ),
inference(resolution,[status(thm)],[c_22,c_67]) ).
tff(c_366,plain,
! [V_U_94] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U_94),v_g(V_U_94),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U_94),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_369,plain,
! [V_U_94] :
( c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U_94),v_g(V_U_94),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U_94),t_b),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_72,c_366]) ).
tff(c_670,plain,
! [V_U_107] : c_lessequals(c_Orderings_Omax(c_minus(v_f(V_U_107),v_g(V_U_107),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U_107),t_b),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_48,c_369]) ).
tff(c_24,plain,
! [V_x_27,V_z_29,T_b_26,V_y_28] :
( c_lessequals(V_x_27,V_z_29,T_b_26)
| ~ c_lessequals(c_Orderings_Omax(V_x_27,V_y_28,T_b_26),V_z_29,T_b_26)
| ~ class_Orderings_Olinorder(T_b_26) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_673,plain,
! [V_U_107] :
( c_lessequals(c_minus(v_f(V_U_107),v_g(V_U_107),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U_107),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(resolution,[status(thm)],[c_670,c_24]) ).
tff(c_721,plain,
! [V_U_112] : c_lessequals(c_minus(v_f(V_U_112),v_g(V_U_112),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U_112),t_b),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_673]) ).
tff(c_12,plain,
! [V_a_9,V_c_11,V_b_10,T_a_8] :
( c_lessequals(V_a_9,c_plus(V_c_11,V_b_10,T_a_8),T_a_8)
| ~ c_lessequals(c_minus(V_a_9,V_b_10,T_a_8),V_c_11,T_a_8)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_8) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_725,plain,
! [V_U_112] :
( c_lessequals(v_f(V_U_112),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U_112),t_b),t_b),v_g(V_U_112),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(resolution,[status(thm)],[c_721,c_12]) ).
tff(c_726,plain,
~ class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(splitLeft,[status(thm)],[c_725]) ).
tff(c_729,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_26,c_726]) ).
tff(c_733,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_729]) ).
tff(c_734,plain,
! [V_U_112] : c_lessequals(v_f(V_U_112),c_plus(c_times(v_c,c_HOL_Oabs(v_h(V_U_112),t_b),t_b),v_g(V_U_112),t_b),t_b),
inference(splitRight,[status(thm)],[c_725]) ).
tff(c_47612,plain,
! [V_U_566] : c_lessequals(v_f(V_U_566),c_plus(v_g(V_U_566),c_times(v_c,c_HOL_Oabs(v_h(V_U_566),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_1404,c_734]) ).
tff(c_4,plain,
! [V_U_2] : ~ c_lessequals(v_f(v_x(V_U_2)),c_plus(v_g(v_x(V_U_2)),c_times(V_U_2,c_HOL_Oabs(v_h(v_x(V_U_2)),t_b),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_47617,plain,
$false,
inference(resolution,[status(thm)],[c_47612,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA030-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu Aug 3 15:30:36 EDT 2023
% 0.10/0.29 % CPUTime :
% 20.42/8.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.42/8.33
% 20.42/8.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.42/8.37
% 20.42/8.37 Inference rules
% 20.42/8.37 ----------------------
% 20.42/8.37 #Ref : 0
% 20.42/8.37 #Sup : 11242
% 20.42/8.37 #Fact : 0
% 20.42/8.37 #Define : 0
% 20.42/8.37 #Split : 1
% 20.42/8.37 #Chain : 0
% 20.42/8.37 #Close : 0
% 20.42/8.37
% 20.42/8.37 Ordering : KBO
% 20.54/8.37
% 20.54/8.37 Simplification rules
% 20.54/8.37 ----------------------
% 20.54/8.37 #Subsume : 1314
% 20.54/8.37 #Demod : 24307
% 20.54/8.37 #Tautology : 2224
% 20.54/8.37 #SimpNegUnit : 0
% 20.54/8.37 #BackRed : 2
% 20.54/8.37
% 20.54/8.37 #Partial instantiations: 0
% 20.54/8.37 #Strategies tried : 1
% 20.54/8.37
% 20.54/8.37 Timing (in seconds)
% 20.54/8.37 ----------------------
% 20.54/8.37 Preprocessing : 0.48
% 20.54/8.37 Parsing : 0.27
% 20.54/8.37 CNF conversion : 0.03
% 20.54/8.37 Main loop : 6.90
% 20.54/8.37 Inferencing : 2.06
% 20.54/8.37 Reduction : 2.95
% 20.54/8.37 Demodulation : 2.60
% 20.54/8.37 BG Simplification : 0.29
% 20.54/8.37 Subsumption : 1.16
% 20.54/8.37 Abstraction : 0.37
% 20.54/8.37 MUC search : 0.00
% 20.54/8.37 Cooper : 0.00
% 20.54/8.37 Total : 7.44
% 20.54/8.37 Index Insertion : 0.00
% 20.54/8.37 Index Deletion : 0.00
% 20.54/8.37 Index Matching : 0.00
% 20.54/8.37 BG Taut test : 0.00
%------------------------------------------------------------------------------