TSTP Solution File: ANA015-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA015-2 : 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 : 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 10:32:47 EDT 2023
% Result : Unsatisfiable 49.13s 15.92s
% Output : CNFRefutation 49.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 68 ( 25 unt; 17 typ; 0 def)
% Number of atoms : 90 ( 4 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 96 ( 57 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 13 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 53 (; 53 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Ofield > class_OrderedGroup_Osemigroup__mult > class_OrderedGroup_Olordered__ab__group__abs > c_times > c_HOL_Oinverse > c_HOL_Oabs > #nlpp > v_x > v_g > v_f > v_d > v_c > t_a > 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(t_a,type,
t_a: $i ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $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_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
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(c_HOL_Oinverse,type,
c_HOL_Oinverse: ( $i * $i ) > $i ).
tff(v_d,type,
v_d: $i ).
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(f_53,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(v_g(V_U),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(f_82,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file(unknown,unknown) ).
tff(f_76,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Oordered__idom(T) ),
file(unknown,unknown) ).
tff(f_40,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_56,axiom,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U)),t_a),t_a),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(f_51,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_81,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_30,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_66,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file(unknown,unknown) ).
tff(f_35,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_10,plain,
! [V_U_14] : c_lessequals(c_HOL_Oabs(v_g(V_U_14),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U_14),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_24,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_20,plain,
! [T_19] :
( class_Ring__and__Field_Opordered__semiring(T_19)
| ~ class_Ring__and__Field_Oordered__field(T_19) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_18,plain,
! [T_18] :
( class_Ring__and__Field_Oordered__idom(T_18)
| ~ class_Ring__and__Field_Oordered__field(T_18) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_6,plain,
! [V_a_8,T_a_7,V_b_9] :
( ( c_times(c_HOL_Oabs(V_a_8,T_a_7),c_HOL_Oabs(V_b_9,T_a_7),T_a_7) = c_HOL_Oabs(c_times(V_a_8,V_b_9,T_a_7),T_a_7) )
| ~ class_Ring__and__Field_Oordered__idom(T_a_7) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_71,plain,
! [V_U_36] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U_36)),t_a),t_a),c_times(V_U_36,c_HOL_Oabs(v_f(v_x(V_U_36)),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_75,plain,
! [V_a_8] :
( ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_HOL_Oabs(V_a_8,t_a))),t_a),t_a),c_HOL_Oabs(c_times(V_a_8,v_f(v_x(c_HOL_Oabs(V_a_8,t_a))),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_71]) ).
tff(c_183,plain,
~ class_Ring__and__Field_Oordered__idom(t_a),
inference(splitLeft,[status(thm)],[c_75]) ).
tff(c_261,plain,
~ class_Ring__and__Field_Oordered__field(t_a),
inference(resolution,[status(thm)],[c_18,c_183]) ).
tff(c_265,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_261]) ).
tff(c_267,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(splitRight,[status(thm)],[c_75]) ).
tff(c_82,plain,
! [V_c_37,V_a_38,T_a_39,V_b_40] :
( c_lessequals(c_times(V_c_37,V_a_38,T_a_39),c_times(V_c_37,V_b_40,T_a_39),T_a_39)
| ~ c_lessequals(c_0,V_c_37,T_a_39)
| ~ c_lessequals(V_a_38,V_b_40,T_a_39)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_39) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_891,plain,
! [V_a_84,V_b_85,T_a_86,V_b_87] :
( c_lessequals(c_HOL_Oabs(c_times(V_a_84,V_b_85,T_a_86),T_a_86),c_times(c_HOL_Oabs(V_a_84,T_a_86),V_b_87,T_a_86),T_a_86)
| ~ c_lessequals(c_0,c_HOL_Oabs(V_a_84,T_a_86),T_a_86)
| ~ c_lessequals(c_HOL_Oabs(V_b_85,T_a_86),V_b_87,T_a_86)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_86)
| ~ class_Ring__and__Field_Oordered__idom(T_a_86) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_82]) ).
tff(c_12,plain,
! [V_U_15] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U_15)),t_a),t_a),c_times(V_U_15,c_HOL_Oabs(v_f(v_x(V_U_15)),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_899,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(resolution,[status(thm)],[c_891,c_12]) ).
tff(c_951,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(demodulation,[status(thm),theory(equality)],[c_267,c_899]) ).
tff(c_1031,plain,
~ class_Ring__and__Field_Opordered__semiring(t_a),
inference(splitLeft,[status(thm)],[c_951]) ).
tff(c_1034,plain,
~ class_Ring__and__Field_Oordered__field(t_a),
inference(resolution,[status(thm)],[c_20,c_1031]) ).
tff(c_1038,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_1034]) ).
tff(c_1040,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(splitRight,[status(thm)],[c_951]) ).
tff(c_25,plain,
! [T_21] :
( class_OrderedGroup_Olordered__ab__group__abs(T_21)
| ~ class_Ring__and__Field_Oordered__field(T_21) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_29,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_24,c_25]) ).
tff(c_2,plain,
! [V_a_2,T_a_1] :
( c_lessequals(c_0,c_HOL_Oabs(V_a_2,T_a_1),T_a_1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_1) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_1039,plain,
( ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
inference(splitRight,[status(thm)],[c_951]) ).
tff(c_1120,plain,
~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a),
inference(splitLeft,[status(thm)],[c_1039]) ).
tff(c_1123,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_2,c_1120]) ).
tff(c_1127,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_29,c_1123]) ).
tff(c_1129,plain,
c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a),
inference(splitRight,[status(thm)],[c_1039]) ).
tff(c_31,plain,
! [T_23] :
( class_Ring__and__Field_Ofield(T_23)
| ~ class_Ring__and__Field_Oordered__field(T_23) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_35,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[c_24,c_31]) ).
tff(c_37,plain,
! [T_25] :
( class_OrderedGroup_Osemigroup__mult(T_25)
| ~ class_Ring__and__Field_Ofield(T_25) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_41,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[status(thm)],[c_35,c_37]) ).
tff(c_4,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_35]) ).
tff(c_79,plain,
! [V_a_4,V_b_5] :
( ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),c_times(V_a_4,c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),t_a),t_a)
| ~ class_OrderedGroup_Osemigroup__mult(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_71]) ).
tff(c_81,plain,
! [V_a_4,V_b_5] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),c_times(V_a_4,c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(V_a_4,V_b_5,t_a))),t_a),t_a),t_a),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_41,c_79]) ).
tff(c_895,plain,
! [V_b_5] :
( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(resolution,[status(thm)],[c_891,c_81]) ).
tff(c_948,plain,
! [V_b_5] :
( ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),c_times(V_b_5,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_5,t_a))),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(demodulation,[status(thm),theory(equality)],[c_267,c_895]) ).
tff(c_101716,plain,
! [V_b_596] : ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_596,t_a))),t_a),c_times(V_b_596,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),V_b_596,t_a))),t_a),t_a),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_1040,c_1129,c_948]) ).
tff(c_102135,plain,
$false,
inference(resolution,[status(thm)],[c_10,c_101716]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ANA015-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n003.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 15:32:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 49.13/15.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.13/15.93
% 49.13/15.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.30/15.96
% 49.30/15.96 Inference rules
% 49.30/15.96 ----------------------
% 49.30/15.96 #Ref : 0
% 49.30/15.96 #Sup : 23335
% 49.30/15.96 #Fact : 0
% 49.30/15.96 #Define : 0
% 49.30/15.96 #Split : 3
% 49.30/15.96 #Chain : 0
% 49.30/15.96 #Close : 0
% 49.30/15.96
% 49.30/15.96 Ordering : KBO
% 49.30/15.96
% 49.30/15.96 Simplification rules
% 49.30/15.96 ----------------------
% 49.30/15.96 #Subsume : 337
% 49.30/15.96 #Demod : 42217
% 49.30/15.96 #Tautology : 172
% 49.30/15.96 #SimpNegUnit : 0
% 49.30/15.96 #BackRed : 0
% 49.30/15.96
% 49.30/15.96 #Partial instantiations: 0
% 49.30/15.96 #Strategies tried : 1
% 49.30/15.96
% 49.30/15.96 Timing (in seconds)
% 49.30/15.96 ----------------------
% 49.30/15.96 Preprocessing : 0.44
% 49.30/15.96 Parsing : 0.24
% 49.30/15.96 CNF conversion : 0.02
% 49.30/15.96 Main loop : 14.47
% 49.30/15.96 Inferencing : 7.22
% 49.30/15.96 Reduction : 2.75
% 49.30/15.96 Demodulation : 2.25
% 49.30/15.96 BG Simplification : 0.84
% 49.30/15.96 Subsumption : 3.12
% 49.30/15.96 Abstraction : 0.90
% 49.30/15.96 MUC search : 0.00
% 49.30/15.96 Cooper : 0.00
% 49.30/15.96 Total : 14.97
% 49.30/15.96 Index Insertion : 0.00
% 49.30/15.96 Index Deletion : 0.00
% 49.30/15.97 Index Matching : 0.00
% 49.30/15.97 BG Taut test : 0.00
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