TSTP Solution File: ANA017-2 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA017-2 : 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 : n009.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 5.99s 2.50s
% Output : CNFRefutation 6.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 55 ( 20 unt; 14 typ; 0 def)
% Number of atoms : 75 ( 4 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 83 ( 49 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 48 (; 48 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Oordered__idom > class_OrderedGroup_Osemigroup__mult > class_OrderedGroup_Olordered__ab__group__abs > c_times > c_HOL_Oabs > #nlpp > v_x > v_f > v_b > v_ca > v_c > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_c,type,
v_c: $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(v_b,type,
v_b: $i > $i ).
tff(class_OrderedGroup_Osemigroup__mult,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(v_ca,type,
v_ca: $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_b(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_31,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_67,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_57,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(c_times(v_c,v_b(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_72,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_36,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_62,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file(unknown,unknown) ).
tff(f_41,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(c_2,plain,
! [V_U_1] : c_lessequals(c_HOL_Oabs(v_b(V_U_1),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U_1),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_6,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_18,plain,
! [T_17] :
( class_Ring__and__Field_Opordered__semiring(T_17)
| ~ class_Ring__and__Field_Oordered__idom(T_17) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_12,plain,
! [V_a_10,T_a_9,V_b_11] :
( ( c_times(c_HOL_Oabs(V_a_10,T_a_9),c_HOL_Oabs(V_b_11,T_a_9),T_a_9) = c_HOL_Oabs(c_times(V_a_10,V_b_11,T_a_9),T_a_9) )
| ~ class_Ring__and__Field_Oordered__idom(T_a_9) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_74,plain,
! [V_c_33,V_a_34,T_a_35,V_b_36] :
( c_lessequals(c_times(V_c_33,V_a_34,T_a_35),c_times(V_c_33,V_b_36,T_a_35),T_a_35)
| ~ c_lessequals(c_0,V_c_33,T_a_35)
| ~ c_lessequals(V_a_34,V_b_36,T_a_35)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_35) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_798,plain,
! [V_a_75,V_b_76,T_a_77,V_b_78] :
( c_lessequals(c_HOL_Oabs(c_times(V_a_75,V_b_76,T_a_77),T_a_77),c_times(c_HOL_Oabs(V_a_75,T_a_77),V_b_78,T_a_77),T_a_77)
| ~ c_lessequals(c_0,c_HOL_Oabs(V_a_75,T_a_77),T_a_77)
| ~ c_lessequals(c_HOL_Oabs(V_b_76,T_a_77),V_b_78,T_a_77)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_77)
| ~ class_Ring__and__Field_Oordered__idom(T_a_77) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_74]) ).
tff(c_4,plain,
! [V_U_2] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(V_U_2)),t_b),t_b),c_times(V_U_2,c_HOL_Oabs(v_f(v_x(V_U_2)),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_806,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_HOL_Oabs(v_c,t_b))),t_b),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(resolution,[status(thm)],[c_798,c_4]) ).
tff(c_858,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_HOL_Oabs(v_c,t_b))),t_b),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_806]) ).
tff(c_859,plain,
~ class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitLeft,[status(thm)],[c_858]) ).
tff(c_941,plain,
~ class_Ring__and__Field_Oordered__idom(t_b),
inference(resolution,[status(thm)],[c_18,c_859]) ).
tff(c_945,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_941]) ).
tff(c_947,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitRight,[status(thm)],[c_858]) ).
tff(c_21,plain,
! [T_19] :
( class_OrderedGroup_Olordered__ab__group__abs(T_19)
| ~ class_Ring__and__Field_Oordered__idom(T_19) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_25,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_6,c_21]) ).
tff(c_8,plain,
! [V_a_4,T_a_3] :
( c_lessequals(c_0,c_HOL_Oabs(V_a_4,T_a_3),T_a_3)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_3) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_946,plain,
( ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_HOL_Oabs(v_c,t_b))),t_b),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b) ),
inference(splitRight,[status(thm)],[c_858]) ).
tff(c_948,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b),
inference(splitLeft,[status(thm)],[c_946]) ).
tff(c_951,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_8,c_948]) ).
tff(c_955,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25,c_951]) ).
tff(c_957,plain,
c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b),
inference(splitRight,[status(thm)],[c_946]) ).
tff(c_27,plain,
! [T_21] :
( class_OrderedGroup_Osemigroup__mult(T_21)
| ~ class_Ring__and__Field_Oordered__idom(T_21) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_31,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[status(thm)],[c_6,c_27]) ).
tff(c_10,plain,
! [V_a_6,V_b_7,T_a_5,V_c_8] :
( ( c_times(c_times(V_a_6,V_b_7,T_a_5),V_c_8,T_a_5) = c_times(V_a_6,c_times(V_b_7,V_c_8,T_a_5),T_a_5) )
| ~ class_OrderedGroup_Osemigroup__mult(T_a_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_61,plain,
! [V_U_32] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(V_U_32)),t_b),t_b),c_times(V_U_32,c_HOL_Oabs(v_f(v_x(V_U_32)),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_65,plain,
! [V_a_6,V_b_7] :
( ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(V_a_6,V_b_7,t_b))),t_b),t_b),c_times(V_a_6,c_times(V_b_7,c_HOL_Oabs(v_f(v_x(c_times(V_a_6,V_b_7,t_b))),t_b),t_b),t_b),t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_61]) ).
tff(c_71,plain,
! [V_a_6,V_b_7] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_b(v_x(c_times(V_a_6,V_b_7,t_b))),t_b),t_b),c_times(V_a_6,c_times(V_b_7,c_HOL_Oabs(v_f(v_x(c_times(V_a_6,V_b_7,t_b))),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_31,c_65]) ).
tff(c_802,plain,
! [V_b_7] :
( ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),V_b_7,t_b))),t_b),c_times(V_b_7,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),V_b_7,t_b))),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(resolution,[status(thm)],[c_798,c_71]) ).
tff(c_855,plain,
! [V_b_7] :
( ~ c_lessequals(c_0,c_HOL_Oabs(v_c,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),V_b_7,t_b))),t_b),c_times(V_b_7,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),V_b_7,t_b))),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_802]) ).
tff(c_3127,plain,
! [V_b_135] : ~ c_lessequals(c_HOL_Oabs(v_b(v_x(c_times(c_HOL_Oabs(v_c,t_b),V_b_135,t_b))),t_b),c_times(V_b_135,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(v_c,t_b),V_b_135,t_b))),t_b),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_947,c_957,c_855]) ).
tff(c_3234,plain,
$false,
inference(resolution,[status(thm)],[c_2,c_3127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA017-2 : 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
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:22:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.99/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.31/2.51
% 6.31/2.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.31/2.54
% 6.31/2.54 Inference rules
% 6.31/2.54 ----------------------
% 6.31/2.54 #Ref : 0
% 6.31/2.54 #Sup : 804
% 6.31/2.54 #Fact : 0
% 6.31/2.54 #Define : 0
% 6.31/2.54 #Split : 2
% 6.31/2.54 #Chain : 0
% 6.31/2.54 #Close : 0
% 6.31/2.54
% 6.31/2.54 Ordering : KBO
% 6.31/2.54
% 6.31/2.54 Simplification rules
% 6.31/2.54 ----------------------
% 6.31/2.54 #Subsume : 14
% 6.31/2.54 #Demod : 544
% 6.31/2.54 #Tautology : 30
% 6.31/2.54 #SimpNegUnit : 0
% 6.31/2.54 #BackRed : 0
% 6.31/2.54
% 6.31/2.54 #Partial instantiations: 0
% 6.31/2.54 #Strategies tried : 1
% 6.31/2.54
% 6.31/2.54 Timing (in seconds)
% 6.31/2.54 ----------------------
% 6.31/2.54 Preprocessing : 0.44
% 6.31/2.54 Parsing : 0.24
% 6.31/2.54 CNF conversion : 0.02
% 6.31/2.54 Main loop : 1.03
% 6.31/2.55 Inferencing : 0.43
% 6.31/2.55 Reduction : 0.26
% 6.31/2.55 Demodulation : 0.20
% 6.31/2.55 BG Simplification : 0.07
% 6.31/2.55 Subsumption : 0.21
% 6.31/2.55 Abstraction : 0.06
% 6.31/2.55 MUC search : 0.00
% 6.31/2.55 Cooper : 0.00
% 6.31/2.55 Total : 1.53
% 6.31/2.55 Index Insertion : 0.00
% 6.31/2.55 Index Deletion : 0.00
% 6.31/2.55 Index Matching : 0.00
% 6.31/2.55 BG Taut test : 0.00
%------------------------------------------------------------------------------