TSTP Solution File: ANA019-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA019-2 : 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 : n003.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 10:32:48 EDT 2023
% Result : Unsatisfiable 3.35s 1.89s
% Output : CNFRefutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 34
% Syntax : Number of formulae : 76 ( 26 unt; 19 typ; 0 def)
% Number of atoms : 97 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 96 ( 56 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 14 >; 9 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 38 (; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Olordered__ab__group__abs > class_LOrder_Ojoin__semilorder > c_times > c_minus > c_HOL_Oabs > #nlpp > v_xa > v_h > v_f > c_Suc > v_x > tc_nat > t_a > c_1 > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_xa,type,
v_xa: $i > $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(t_a,type,
t_a: $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(c_0,type,
c_0: $i ).
tff(c_1,type,
c_1: $i ).
tff(c_times,type,
c_times: ( $i * $i * $i ) > $i ).
tff(c_Suc,type,
c_Suc: $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(tc_nat,type,
tc_nat: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_less,type,
c_less: ( $i * $i * $i ) > $o ).
tff(class_LOrder_Ojoin__semilorder,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
tff(v_f,type,
v_f: $i > $i ).
tff(f_36,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file(unknown,unknown) ).
tff(f_94,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_84,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_LOrder_Ojoin__semilorder(T) ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [T] :
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [T_a,V_x,V_y] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [V_U] :
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U)),t_a),c_times(V_U,c_HOL_Oabs(v_h(v_xa(V_U)),t_a),t_a),t_a)
| ~ c_less(c_0,V_U,t_a) ),
file(unknown,unknown) ).
tff(f_27,axiom,
c_less(c_0,v_x,t_a),
file(unknown,unknown) ).
tff(f_89,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file(unknown,unknown) ).
tff(f_74,axiom,
! [T_a,V_b,V_a] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [T_a] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ( c_HOL_Oabs(c_0,T_a) = c_0 ) ),
file(unknown,unknown) ).
tff(f_26,axiom,
v_f(c_0) = c_0,
file(unknown,unknown) ).
tff(f_45,axiom,
! [V_n] :
( c_less(c_0,V_n,tc_nat)
| ( V_n = c_0 ) ),
file(unknown,unknown) ).
tff(f_41,axiom,
! [V_x] :
( ~ c_less(c_0,V_x,tc_nat)
| ( V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(c_10,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_35,plain,
! [T_18] :
( class_OrderedGroup_Olordered__ab__group__abs(T_18)
| ~ class_Ring__and__Field_Oordered__idom(T_18) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_39,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_10,c_35]) ).
tff(c_18,plain,
! [V_a_7,T_a_6] :
( c_lessequals(c_0,c_HOL_Oabs(V_a_7,T_a_6),T_a_6)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_6) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_42,plain,
! [T_21] :
( class_LOrder_Ojoin__semilorder(T_21)
| ~ class_Ring__and__Field_Oordered__idom(T_21) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_46,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(resolution,[status(thm)],[c_10,c_42]) ).
tff(c_24,plain,
! [T_14] :
( class_Orderings_Oorder(T_14)
| ~ class_LOrder_Ojoin__semilorder(T_14) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_20,plain,
! [V_x_9,V_y_10,T_a_8] :
( c_lessequals(V_x_9,V_y_10,T_a_8)
| ~ c_less(V_x_9,V_y_10,T_a_8)
| ~ class_Orderings_Oorder(T_a_8) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_81,plain,
! [V_U_34] :
( ~ c_less(c_0,V_U_34,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U_34)),t_a),c_times(V_U_34,c_HOL_Oabs(v_h(v_xa(V_U_34)),t_a),t_a),t_a) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_85,plain,
! [V_U_34] :
( ~ c_less(c_0,V_U_34,t_a)
| ~ c_less(c_HOL_Oabs(v_f(v_xa(V_U_34)),t_a),c_times(V_U_34,c_HOL_Oabs(v_h(v_xa(V_U_34)),t_a),t_a),t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[c_20,c_81]) ).
tff(c_104,plain,
~ class_Orderings_Oorder(t_a),
inference(splitLeft,[status(thm)],[c_85]) ).
tff(c_107,plain,
~ class_LOrder_Ojoin__semilorder(t_a),
inference(resolution,[status(thm)],[c_24,c_104]) ).
tff(c_111,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_46,c_107]) ).
tff(c_113,plain,
class_Orderings_Oorder(t_a),
inference(splitRight,[status(thm)],[c_85]) ).
tff(c_4,plain,
c_less(c_0,v_x,t_a),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_28,plain,
! [T_16] :
( class_Ring__and__Field_Opordered__cancel__semiring(T_16)
| ~ class_Ring__and__Field_Oordered__idom(T_16) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_22,plain,
! [V_a_13,V_b_12,T_a_11] :
( c_lessequals(c_0,c_times(V_a_13,V_b_12,T_a_11),T_a_11)
| ~ c_lessequals(c_0,V_a_13,T_a_11)
| ~ c_lessequals(c_0,V_b_12,T_a_11)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a_11) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_47,plain,
! [T_a_22] :
( ( c_HOL_Oabs(c_0,T_a_22) = c_0 )
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_22) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_51,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(resolution,[status(thm)],[c_39,c_47]) ).
tff(c_2,plain,
v_f(c_0) = c_0,
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_14,plain,
! [V_n_4] :
( ( c_0 = V_n_4 )
| c_less(c_0,V_n_4,tc_nat) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_12,plain,
! [V_x_3] :
( ( c_Suc(c_minus(V_x_3,c_1,tc_nat)) = V_x_3 )
| ~ c_less(c_0,V_x_3,tc_nat) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_73,plain,
! [V_U_30] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U_30)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U_30)),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_86,plain,
! [V_x_35] :
( c_lessequals(c_HOL_Oabs(v_f(V_x_35),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(c_minus(V_x_35,c_1,tc_nat))),t_a),t_a),t_a)
| ~ c_less(c_0,V_x_35,tc_nat) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_73]) ).
tff(c_115,plain,
! [V_x_38] :
( c_lessequals(c_HOL_Oabs(v_f(V_x_38),t_a),c_times(v_x,c_HOL_Oabs(v_h(V_x_38),t_a),t_a),t_a)
| ~ c_less(c_0,V_x_38,tc_nat)
| ~ c_less(c_0,V_x_38,tc_nat) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_86]) ).
tff(c_8,plain,
! [V_U_2] :
( ~ c_less(c_0,V_U_2,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U_2)),t_a),c_times(V_U_2,c_HOL_Oabs(v_h(v_xa(V_U_2)),t_a),t_a),t_a) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_119,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_less(c_0,v_xa(v_x),tc_nat) ),
inference(resolution,[status(thm)],[c_115,c_8]) ).
tff(c_125,plain,
~ c_less(c_0,v_xa(v_x),tc_nat),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_119]) ).
tff(c_130,plain,
v_xa(v_x) = c_0,
inference(resolution,[status(thm)],[c_14,c_125]) ).
tff(c_144,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_8]) ).
tff(c_154,plain,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_51,c_2,c_130,c_4,c_144]) ).
tff(c_162,plain,
( ~ c_lessequals(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
inference(resolution,[status(thm)],[c_22,c_154]) ).
tff(c_166,plain,
~ class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(splitLeft,[status(thm)],[c_162]) ).
tff(c_169,plain,
~ class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[status(thm)],[c_28,c_166]) ).
tff(c_173,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_169]) ).
tff(c_174,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ c_lessequals(c_0,v_x,t_a) ),
inference(splitRight,[status(thm)],[c_162]) ).
tff(c_176,plain,
~ c_lessequals(c_0,v_x,t_a),
inference(splitLeft,[status(thm)],[c_174]) ).
tff(c_179,plain,
( ~ c_less(c_0,v_x,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[c_20,c_176]) ).
tff(c_183,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_113,c_4,c_179]) ).
tff(c_184,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a),
inference(splitRight,[status(thm)],[c_174]) ).
tff(c_191,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_18,c_184]) ).
tff(c_198,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_39,c_191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.13 % Problem : ANA019-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % 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
% 0.15/0.36 % Computer : n003.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 15:28:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.35/1.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.35/1.90
% 3.35/1.90 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.54/1.94
% 3.54/1.94 Inference rules
% 3.54/1.94 ----------------------
% 3.54/1.94 #Ref : 0
% 3.54/1.94 #Sup : 33
% 3.54/1.94 #Fact : 0
% 3.54/1.94 #Define : 0
% 3.54/1.94 #Split : 4
% 3.54/1.94 #Chain : 0
% 3.54/1.94 #Close : 0
% 3.54/1.94
% 3.54/1.94 Ordering : KBO
% 3.54/1.94
% 3.54/1.94 Simplification rules
% 3.54/1.94 ----------------------
% 3.54/1.94 #Subsume : 7
% 3.54/1.94 #Demod : 28
% 3.54/1.94 #Tautology : 9
% 3.54/1.94 #SimpNegUnit : 0
% 3.54/1.94 #BackRed : 1
% 3.54/1.94
% 3.54/1.94 #Partial instantiations: 0
% 3.54/1.94 #Strategies tried : 1
% 3.54/1.94
% 3.54/1.94 Timing (in seconds)
% 3.54/1.94 ----------------------
% 3.54/1.94 Preprocessing : 0.48
% 3.54/1.94 Parsing : 0.24
% 3.54/1.94 CNF conversion : 0.03
% 3.54/1.94 Main loop : 0.37
% 3.54/1.94 Inferencing : 0.15
% 3.54/1.94 Reduction : 0.09
% 3.54/1.94 Demodulation : 0.07
% 3.54/1.94 BG Simplification : 0.02
% 3.54/1.94 Subsumption : 0.08
% 3.54/1.94 Abstraction : 0.01
% 3.54/1.94 MUC search : 0.00
% 3.54/1.94 Cooper : 0.00
% 3.54/1.94 Total : 0.92
% 3.54/1.94 Index Insertion : 0.00
% 3.54/1.94 Index Deletion : 0.00
% 3.54/1.94 Index Matching : 0.00
% 3.54/1.94 BG Taut test : 0.00
%------------------------------------------------------------------------------