TSTP Solution File: ANA034-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA034-2 : 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 : n005.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 10:32:51 EDT 2023
% Result : Unsatisfiable 3.71s 2.00s
% Output : CNFRefutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of formulae : 90 ( 38 unt; 18 typ; 0 def)
% Number of atoms : 155 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 188 ( 105 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 13 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 60 (; 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Olordered__ab__group__abs > c_times > c_HOL_Oabs > #nlpp > v_g > v_f > v_b > v_a > v_x > v_ca > v_c > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_c,type,
v_c: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(v_a,type,
v_a: $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_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(v_ca,type,
v_ca: $i ).
tff(c_less,type,
c_less: ( $i * $i * $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_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(f_78,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_98,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_71,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_74,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_73,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_30,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_93,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file(unknown,unknown) ).
tff(f_83,axiom,
! [T] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_66,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_77,axiom,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_72,axiom,
c_less(c_0,v_c,t_b),
file(unknown,unknown) ).
tff(f_88,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file(unknown,unknown) ).
tff(f_75,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_58,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_47,axiom,
! [V_a,T_a,V_d,V_c,V_b] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a) ),
file(unknown,unknown) ).
tff(c_22,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_31,plain,
! [T_21] :
( class_OrderedGroup_Olordered__ab__group__abs(T_21)
| ~ class_Ring__and__Field_Oordered__idom(T_21) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_35,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_22,c_31]) ).
tff(c_10,plain,
! [V_a_16,T_a_15] :
( c_lessequals(c_0,c_HOL_Oabs(V_a_16,T_a_15),T_a_15)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_15) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_16,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_14,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_2,plain,
! [V_a_2,T_a_1,V_b_3] :
( ( c_times(c_HOL_Oabs(V_a_2,T_a_1),c_HOL_Oabs(V_b_3,T_a_1),T_a_1) = c_HOL_Oabs(c_times(V_a_2,V_b_3,T_a_1),T_a_1) )
| ~ class_Ring__and__Field_Oordered__idom(T_a_1) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_28,plain,
! [T_19] :
( class_Ring__and__Field_Opordered__semiring(T_19)
| ~ class_Ring__and__Field_Oordered__idom(T_19) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_24,plain,
! [T_17] :
( class_Orderings_Oorder(T_17)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_17) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_8,plain,
! [V_x_13,V_y_14,T_a_12] :
( c_lessequals(V_x_13,V_y_14,T_a_12)
| ~ c_less(V_x_13,V_y_14,T_a_12)
| ~ class_Orderings_Oorder(T_a_12) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_20,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_57,plain,
( ~ c_less(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_8,c_20]) ).
tff(c_69,plain,
~ class_Orderings_Oorder(t_b),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_72,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_24,c_69]) ).
tff(c_76,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_35,c_72]) ).
tff(c_78,plain,
class_Orderings_Oorder(t_b),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_12,plain,
c_less(c_0,v_c,t_b),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_26,plain,
! [T_18] :
( class_Ring__and__Field_Opordered__cancel__semiring(T_18)
| ~ class_Ring__and__Field_Oordered__idom(T_18) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_18,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_6,plain,
! [V_a_11,V_b_10,T_a_9] :
( c_lessequals(c_0,c_times(V_a_11,V_b_10,T_a_9),T_a_9)
| ~ c_lessequals(c_0,V_a_11,T_a_9)
| ~ c_lessequals(c_0,V_b_10,T_a_9)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a_9) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_91,plain,
( c_lessequals(c_0,c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_6]) ).
tff(c_146,plain,
~ class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(splitLeft,[status(thm)],[c_91]) ).
tff(c_149,plain,
~ class_Ring__and__Field_Oordered__idom(t_b),
inference(resolution,[status(thm)],[c_26,c_146]) ).
tff(c_153,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_149]) ).
tff(c_155,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(splitRight,[status(thm)],[c_91]) ).
tff(c_154,plain,
( ~ c_lessequals(c_0,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| c_lessequals(c_0,c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) ),
inference(splitRight,[status(thm)],[c_91]) ).
tff(c_156,plain,
~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(splitLeft,[status(thm)],[c_154]) ).
tff(c_159,plain,
( ~ c_lessequals(c_0,v_c,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(resolution,[status(thm)],[c_6,c_156]) ).
tff(c_165,plain,
( ~ c_lessequals(c_0,v_c,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_155,c_159]) ).
tff(c_178,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b),
inference(splitLeft,[status(thm)],[c_165]) ).
tff(c_184,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_10,c_178]) ).
tff(c_191,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_35,c_184]) ).
tff(c_192,plain,
~ c_lessequals(c_0,v_c,t_b),
inference(splitRight,[status(thm)],[c_165]) ).
tff(c_196,plain,
( ~ c_less(c_0,v_c,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_8,c_192]) ).
tff(c_200,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_78,c_12,c_196]) ).
tff(c_202,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_4,plain,
! [V_b_8,V_a_4,V_d_6,T_a_5,V_c_7] :
( c_lessequals(c_times(V_a_4,V_c_7,T_a_5),c_times(V_b_8,V_d_6,T_a_5),T_a_5)
| ~ c_lessequals(c_0,V_b_8,T_a_5)
| ~ c_lessequals(c_0,V_c_7,T_a_5)
| ~ c_lessequals(V_a_4,V_b_8,T_a_5)
| ~ c_lessequals(V_c_7,V_d_6,T_a_5)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_5) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_85,plain,
! [V_a_4,V_c_7] :
( c_lessequals(c_times(V_a_4,V_c_7,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,V_c_7,t_b)
| ~ c_lessequals(V_a_4,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(V_c_7,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_4]) ).
tff(c_249,plain,
! [V_a_4,V_c_7] :
( c_lessequals(c_times(V_a_4,V_c_7,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,V_c_7,t_b)
| ~ c_lessequals(V_a_4,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(V_c_7,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_202,c_85]) ).
tff(c_250,plain,
~ class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitLeft,[status(thm)],[c_249]) ).
tff(c_253,plain,
~ class_Ring__and__Field_Oordered__idom(t_b),
inference(resolution,[status(thm)],[c_28,c_250]) ).
tff(c_257,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_22,c_253]) ).
tff(c_259,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitRight,[status(thm)],[c_249]) ).
tff(c_62,plain,
! [T_a_41,V_a_40,V_d_39,V_c_42,V_b_43] :
( c_lessequals(c_times(V_a_40,V_c_42,T_a_41),c_times(V_b_43,V_d_39,T_a_41),T_a_41)
| ~ c_lessequals(c_0,V_b_43,T_a_41)
| ~ c_lessequals(c_0,V_c_42,T_a_41)
| ~ c_lessequals(V_a_40,V_b_43,T_a_41)
| ~ c_lessequals(V_c_42,V_d_39,T_a_41)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_41) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_123,plain,
! [V_b_55,T_a_52,V_d_53,V_b_56,V_a_54] :
( c_lessequals(c_HOL_Oabs(c_times(V_a_54,V_b_55,T_a_52),T_a_52),c_times(V_b_56,V_d_53,T_a_52),T_a_52)
| ~ c_lessequals(c_0,V_b_56,T_a_52)
| ~ c_lessequals(c_0,c_HOL_Oabs(V_b_55,T_a_52),T_a_52)
| ~ c_lessequals(c_HOL_Oabs(V_a_54,T_a_52),V_b_56,T_a_52)
| ~ c_lessequals(c_HOL_Oabs(V_b_55,T_a_52),V_d_53,T_a_52)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_52)
| ~ class_Ring__and__Field_Oordered__idom(T_a_52) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_62]) ).
tff(c_126,plain,
( ~ c_lessequals(c_0,c_times(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),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_123,c_20]) ).
tff(c_141,plain,
( ~ c_lessequals(c_0,c_times(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,v_ca,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_126]) ).
tff(c_247,plain,
~ class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitLeft,[status(thm)],[c_141]) ).
tff(c_261,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_259,c_247]) ).
tff(c_263,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(splitRight,[status(thm)],[c_141]) ).
tff(c_415,plain,
! [V_a_89,V_c_90] :
( c_lessequals(c_times(V_a_89,V_c_90,t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,V_c_90,t_b)
| ~ c_lessequals(V_a_89,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(V_c_90,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_263,c_202,c_85]) ).
tff(c_422,plain,
! [V_a_2,V_b_3] :
( c_lessequals(c_HOL_Oabs(c_times(V_a_2,V_b_3,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(V_b_3,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(V_a_2,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(V_b_3,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_415]) ).
tff(c_483,plain,
! [V_a_93,V_b_94] :
( c_lessequals(c_HOL_Oabs(c_times(V_a_93,V_b_94,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(V_b_94,t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(V_a_93,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(V_b_94,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_422]) ).
tff(c_486,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) ),
inference(resolution,[status(thm)],[c_483,c_20]) ).
tff(c_496,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_14,c_486]) ).
tff(c_515,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_10,c_496]) ).
tff(c_522,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_35,c_515]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : ANA034-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % 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 : n005.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 15:25:42 EDT 2023
% 0.15/0.36 % CPUTime :
% 3.71/2.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.71/2.01
% 3.71/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/2.05
% 3.71/2.05 Inference rules
% 3.71/2.05 ----------------------
% 3.71/2.05 #Ref : 0
% 3.71/2.05 #Sup : 87
% 3.71/2.05 #Fact : 0
% 3.71/2.05 #Define : 0
% 3.71/2.05 #Split : 13
% 3.71/2.05 #Chain : 0
% 3.71/2.05 #Close : 0
% 3.71/2.05
% 3.71/2.05 Ordering : KBO
% 3.71/2.05
% 3.71/2.05 Simplification rules
% 3.71/2.05 ----------------------
% 3.71/2.05 #Subsume : 7
% 3.71/2.05 #Demod : 109
% 3.71/2.05 #Tautology : 4
% 3.71/2.05 #SimpNegUnit : 0
% 3.71/2.05 #BackRed : 0
% 3.71/2.05
% 3.71/2.05 #Partial instantiations: 0
% 3.71/2.05 #Strategies tried : 1
% 3.71/2.05
% 3.71/2.05 Timing (in seconds)
% 3.71/2.05 ----------------------
% 3.71/2.06 Preprocessing : 0.46
% 3.71/2.06 Parsing : 0.25
% 3.71/2.06 CNF conversion : 0.02
% 3.71/2.06 Main loop : 0.50
% 3.71/2.06 Inferencing : 0.21
% 3.71/2.06 Reduction : 0.14
% 3.71/2.06 Demodulation : 0.10
% 3.71/2.06 BG Simplification : 0.02
% 3.71/2.06 Subsumption : 0.09
% 3.71/2.06 Abstraction : 0.02
% 3.71/2.06 MUC search : 0.00
% 3.71/2.06 Cooper : 0.00
% 3.71/2.06 Total : 1.02
% 3.71/2.06 Index Insertion : 0.00
% 3.71/2.06 Index Deletion : 0.00
% 3.71/2.06 Index Matching : 0.00
% 3.71/2.06 BG Taut test : 0.00
%------------------------------------------------------------------------------