TSTP Solution File: ANA018-2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA018-2 : 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 : n025.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 4.02s 2.01s
% Output : CNFRefutation 4.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 67 ( 24 unt; 17 typ; 0 def)
% Number of atoms : 95 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 56 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 12 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 61 (; 61 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Osemigroup__mult > class_LOrder_Ojoin__semilorder > c_times > c_HOL_Oabs > #nlpp > v_x > v_g > v_f > v_xa > v_ca > v_c > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_c,type,
v_c: $i ).
tff(v_xa,type,
v_xa: $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_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(class_OrderedGroup_Osemigroup__mult,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(v_ca,type,
v_ca: $i ).
tff(c_less,type,
c_less: ( $i * $i * $i ) > $o ).
tff(class_LOrder_Ojoin__semilorder,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
tff(v_g,type,
v_g: $i > $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(v_x,type,
v_x: $i > $i ).
tff(v_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(f_27,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_33,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_83,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_LOrder_Ojoin__semilorder(T) ),
file(unknown,unknown) ).
tff(f_73,axiom,
! [T] :
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_28,axiom,
c_less(c_0,v_ca,t_b),
file(unknown,unknown) ).
tff(f_57,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_49,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(f_88,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_78,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file(unknown,unknown) ).
tff(f_38,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ 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) ) ),
file(unknown,unknown) ).
tff(f_32,axiom,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(c_2,plain,
! [V_U_1] : c_lessequals(c_HOL_Oabs(v_f(V_U_1),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U_1),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_10,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_28,plain,
! [T_23] :
( class_LOrder_Ojoin__semilorder(T_23)
| ~ class_Ring__and__Field_Oordered__idom(T_23) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_32,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[c_10,c_28]) ).
tff(c_20,plain,
! [T_18] :
( class_Orderings_Oorder(T_18)
| ~ class_LOrder_Ojoin__semilorder(T_18) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_4,plain,
c_less(c_0,v_ca,t_b),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_16,plain,
! [V_x_12,V_y_13,T_a_11] :
( c_lessequals(V_x_12,V_y_13,T_a_11)
| ~ c_less(V_x_12,V_y_13,T_a_11)
| ~ class_Orderings_Oorder(T_a_11) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_42,plain,
! [V_x_31,V_z_32,T_a_33,V_y_34] :
( c_lessequals(V_x_31,V_z_32,T_a_33)
| ~ c_lessequals(V_x_31,V_y_34,T_a_33)
| ~ c_lessequals(V_y_34,V_z_32,T_a_33)
| ~ class_Orderings_Oorder(T_a_33) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_52,plain,
! [V_x_35,V_z_36,T_a_37,V_y_38] :
( c_lessequals(V_x_35,V_z_36,T_a_37)
| ~ c_lessequals(V_y_38,V_z_36,T_a_37)
| ~ c_less(V_x_35,V_y_38,T_a_37)
| ~ class_Orderings_Oorder(T_a_37) ),
inference(resolution,[status(thm)],[c_16,c_42]) ).
tff(c_62,plain,
! [V_x_39,V_y_40,T_a_41,V_x_42] :
( c_lessequals(V_x_39,V_y_40,T_a_41)
| ~ c_less(V_x_39,V_x_42,T_a_41)
| ~ c_less(V_x_42,V_y_40,T_a_41)
| ~ class_Orderings_Oorder(T_a_41) ),
inference(resolution,[status(thm)],[c_16,c_52]) ).
tff(c_65,plain,
! [V_y_40] :
( c_lessequals(c_0,V_y_40,t_b)
| ~ c_less(v_ca,V_y_40,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_4,c_62]) ).
tff(c_66,plain,
~ class_Orderings_Oorder(t_b),
inference(splitLeft,[status(thm)],[c_65]) ).
tff(c_84,plain,
~ class_LOrder_Ojoin__semilorder(t_b),
inference(resolution,[status(thm)],[c_20,c_66]) ).
tff(c_88,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_84]) ).
tff(c_90,plain,
class_Orderings_Oorder(t_b),
inference(splitRight,[status(thm)],[c_65]) ).
tff(c_26,plain,
! [T_21] :
( class_Ring__and__Field_Opordered__semiring(T_21)
| ~ class_Ring__and__Field_Oordered__idom(T_21) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_18,plain,
! [V_c_17,V_a_15,T_a_14,V_b_16] :
( c_lessequals(c_times(V_c_17,V_a_15,T_a_14),c_times(V_c_17,V_b_16,T_a_14),T_a_14)
| ~ c_lessequals(c_0,V_c_17,T_a_14)
| ~ c_lessequals(V_a_15,V_b_16,T_a_14)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_14) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_6,plain,
! [V_U_2] : c_lessequals(c_HOL_Oabs(v_x(V_U_2),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U_2),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_50,plain,
! [V_U_2,V_z_32] :
( c_lessequals(c_HOL_Oabs(v_x(V_U_2),t_b),V_z_32,t_b)
| ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U_2),t_b),t_b),V_z_32,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_6,c_42]) ).
tff(c_279,plain,
! [V_U_75,V_z_76] :
( c_lessequals(c_HOL_Oabs(v_x(V_U_75),t_b),V_z_76,t_b)
| ~ c_lessequals(c_times(v_ca,c_HOL_Oabs(v_f(V_U_75),t_b),t_b),V_z_76,t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_90,c_50]) ).
tff(c_292,plain,
! [V_U_75,V_b_16] :
( c_lessequals(c_HOL_Oabs(v_x(V_U_75),t_b),c_times(v_ca,V_b_16,t_b),t_b)
| ~ c_lessequals(c_0,v_ca,t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(V_U_75),t_b),V_b_16,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(resolution,[status(thm)],[c_18,c_279]) ).
tff(c_540,plain,
~ class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitLeft,[status(thm)],[c_292]) ).
tff(c_543,plain,
~ class_Ring__and__Field_Oordered__idom(t_b),
inference(resolution,[status(thm)],[c_26,c_540]) ).
tff(c_547,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_543]) ).
tff(c_548,plain,
! [V_U_75,V_b_16] :
( ~ c_lessequals(c_0,v_ca,t_b)
| c_lessequals(c_HOL_Oabs(v_x(V_U_75),t_b),c_times(v_ca,V_b_16,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(V_U_75),t_b),V_b_16,t_b) ),
inference(splitRight,[status(thm)],[c_292]) ).
tff(c_550,plain,
~ c_lessequals(c_0,v_ca,t_b),
inference(splitLeft,[status(thm)],[c_548]) ).
tff(c_559,plain,
( ~ c_less(c_0,v_ca,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_16,c_550]) ).
tff(c_565,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_90,c_4,c_559]) ).
tff(c_809,plain,
! [V_U_136,V_b_137] :
( c_lessequals(c_HOL_Oabs(v_x(V_U_136),t_b),c_times(v_ca,V_b_137,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_f(V_U_136),t_b),V_b_137,t_b) ),
inference(splitRight,[status(thm)],[c_548]) ).
tff(c_34,plain,
! [T_25] :
( class_OrderedGroup_Osemigroup__mult(T_25)
| ~ class_Ring__and__Field_Oordered__idom(T_25) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_38,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[status(thm)],[c_10,c_34]) ).
tff(c_12,plain,
! [V_a_4,V_b_5,T_a_3,V_c_6] :
( ( c_times(c_times(V_a_4,V_b_5,T_a_3),V_c_6,T_a_3) = c_times(V_a_4,c_times(V_b_5,V_c_6,T_a_3),T_a_3) )
| ~ class_OrderedGroup_Osemigroup__mult(T_a_3) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_8,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_153,plain,
( ~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_8]) ).
tff(c_159,plain,
~ c_lessequals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_153]) ).
tff(c_814,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_xa),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
inference(resolution,[status(thm)],[c_809,c_159]) ).
tff(c_825,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_814]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA018-2 : 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 : n025.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 15:38:04 EDT 2023
% 0.15/0.36 % CPUTime :
% 4.02/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/2.02
% 4.02/2.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.31/2.05
% 4.31/2.05 Inference rules
% 4.31/2.05 ----------------------
% 4.31/2.05 #Ref : 0
% 4.31/2.05 #Sup : 175
% 4.31/2.05 #Fact : 0
% 4.31/2.05 #Define : 0
% 4.31/2.05 #Split : 6
% 4.31/2.05 #Chain : 0
% 4.31/2.05 #Close : 0
% 4.31/2.05
% 4.31/2.05 Ordering : KBO
% 4.31/2.05
% 4.31/2.05 Simplification rules
% 4.31/2.05 ----------------------
% 4.31/2.05 #Subsume : 33
% 4.31/2.05 #Demod : 64
% 4.31/2.05 #Tautology : 10
% 4.31/2.05 #SimpNegUnit : 0
% 4.31/2.05 #BackRed : 0
% 4.31/2.05
% 4.31/2.05 #Partial instantiations: 0
% 4.31/2.05 #Strategies tried : 1
% 4.31/2.05
% 4.31/2.05 Timing (in seconds)
% 4.31/2.05 ----------------------
% 4.31/2.06 Preprocessing : 0.45
% 4.31/2.06 Parsing : 0.25
% 4.31/2.06 CNF conversion : 0.03
% 4.31/2.06 Main loop : 0.54
% 4.31/2.06 Inferencing : 0.23
% 4.31/2.06 Reduction : 0.13
% 4.31/2.06 Demodulation : 0.10
% 4.31/2.06 BG Simplification : 0.03
% 4.31/2.06 Subsumption : 0.11
% 4.31/2.06 Abstraction : 0.02
% 4.31/2.06 MUC search : 0.00
% 4.31/2.06 Cooper : 0.00
% 4.31/2.06 Total : 1.05
% 4.31/2.06 Index Insertion : 0.00
% 4.31/2.06 Index Deletion : 0.00
% 4.31/2.06 Index Matching : 0.00
% 4.31/2.06 BG Taut test : 0.00
%------------------------------------------------------------------------------