%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA029-2 : TPTP v9.0.0. 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 : n008.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 : Wed Apr 9 05:37:37 PM UTC 2025
% Result : Unsatisfiable 4.88s 2.19s
% Output : CNFRefutation 4.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 125 ( 68 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 62 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__abs > c_minus > c_Orderings_Omax > c_HOL_Oabs > #nlpp > v_k > v_g > v_f > v_x > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $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(c_0,type,
c_0: $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(c_less,type,
c_less: ( $i * $i * $i ) > $o ).
tff(c_Orderings_Omax,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(v_g,type,
v_g: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(v_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(v_k,type,
v_k: $i > $i ).
tff(f_30,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_108,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file(unknown,unknown) ).
tff(f_93,axiom,
! [T] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_88,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_27,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file(unknown,unknown) ).
tff(f_98,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [T_a,V_y,V_x] :
( ~ class_Orderings_Olinorder(T_a)
| c_less(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_43,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| c_lessequals(V_a,V_b,T_a) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_35,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_69,axiom,
! [T_b,V_y,V_z,V_x] :
( ~ class_Orderings_Olinorder(T_b)
| ~ c_lessequals(V_y,V_z,T_b)
| ~ c_lessequals(V_x,V_z,T_b)
| c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b) ),
file(unknown,unknown) ).
tff(f_29,axiom,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_51,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a) ),
file(unknown,unknown) ).
tff(f_80,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(c_6,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_40,plain,
! [T_30] :
( class_OrderedGroup_Opordered__ab__group__add(T_30)
| ~ class_Ring__and__Field_Oordered__idom(T_30) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_44,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[c_6,c_40]) ).
tff(c_22,plain,
! [T_23] :
( class_Orderings_Oorder(T_23)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_23) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_53,plain,
! [V_x_36,V_y_37,T_a_38] :
( c_lessequals(V_x_36,V_y_37,T_a_38)
| ~ c_less(V_x_36,V_y_37,T_a_38)
| ~ class_Orderings_Oorder(T_a_38) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_2,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_57,plain,
( ~ c_less(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_53,c_2]) ).
tff(c_58,plain,
~ class_Orderings_Oorder(t_b),
inference(splitLeft,[status(thm)],[c_57]) ).
tff(c_61,plain,
~ class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[c_22,c_58]) ).
tff(c_65,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44,c_61]) ).
tff(c_67,plain,
class_Orderings_Oorder(t_b),
inference(splitRight,[status(thm)],[c_57]) ).
tff(c_34,plain,
! [T_28] :
( class_Orderings_Olinorder(T_28)
| ~ class_Ring__and__Field_Oordered__idom(T_28) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_38,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_6,c_34]) ).
tff(c_46,plain,
! [V_x_33,V_y_34,T_a_35] :
( c_lessequals(V_x_33,V_y_34,T_a_35)
| c_less(V_y_34,V_x_33,T_a_35)
| ~ class_Orderings_Olinorder(T_a_35) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_49,plain,
( c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(resolution,[status(thm)],[c_46,c_2]) ).
tff(c_52,plain,
c_less(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_49]) ).
tff(c_20,plain,
! [V_x_21,V_y_22,T_a_20] :
( c_lessequals(V_x_21,V_y_22,T_a_20)
| ~ c_less(V_x_21,V_y_22,T_a_20)
| ~ class_Orderings_Oorder(T_a_20) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_68,plain,
! [V_a_39,V_b_40,T_a_41] :
( c_lessequals(V_a_39,V_b_40,T_a_41)
| ~ c_lessequals(c_minus(V_a_39,V_b_40,T_a_41),c_0,T_a_41)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_41) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_190,plain,
! [V_a_71,V_b_72,T_a_73] :
( c_lessequals(V_a_71,V_b_72,T_a_73)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_73)
| ~ c_less(c_minus(V_a_71,V_b_72,T_a_73),c_0,T_a_73)
| ~ class_Orderings_Oorder(T_a_73) ),
inference(resolution,[status(thm)],[c_20,c_68]) ).
tff(c_193,plain,
( c_lessequals(v_f(v_x),v_k(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_52,c_190]) ).
tff(c_196,plain,
c_lessequals(v_f(v_x),v_k(v_x),t_b),
inference(demodulation,[status(thm),theory(equality)],[c_67,c_44,c_193]) ).
tff(c_29,plain,
! [T_27] :
( class_OrderedGroup_Olordered__ab__group__abs(T_27)
| ~ class_Ring__and__Field_Oordered__idom(T_27) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_33,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_6,c_29]) ).
tff(c_8,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_35]) ).
tff(c_16,plain,
! [V_x_15,V_y_13,T_b_12,V_z_14] :
( c_lessequals(c_Orderings_Omax(V_x_15,V_y_13,T_b_12),V_z_14,T_b_12)
| ~ c_lessequals(V_x_15,V_z_14,T_b_12)
| ~ c_lessequals(V_y_13,V_z_14,T_b_12)
| ~ class_Orderings_Olinorder(T_b_12) ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_4,plain,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_171,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) ),
inference(resolution,[status(thm)],[c_16,c_4]) ).
tff(c_183,plain,
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_38,c_171]) ).
tff(c_1716,plain,
~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(splitLeft,[status(thm)],[c_183]) ).
tff(c_1742,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_8,c_1716]) ).
tff(c_1761,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_33,c_1742]) ).
tff(c_1763,plain,
c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_12,plain,
! [V_a_7,V_b_8,T_a_6] :
( c_lessequals(c_minus(V_a_7,V_b_8,T_a_6),c_0,T_a_6)
| ~ c_lessequals(V_a_7,V_b_8,T_a_6)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_6) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_84,plain,
! [V_x_45,V_z_46,T_a_47,V_y_48] :
( c_lessequals(V_x_45,V_z_46,T_a_47)
| ~ c_lessequals(V_x_45,V_y_48,T_a_47)
| ~ c_lessequals(V_y_48,V_z_46,T_a_47)
| ~ class_Orderings_Oorder(T_a_47) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_93,plain,
! [V_a_7,V_b_8,T_a_6,V_z_46] :
( c_lessequals(c_minus(V_a_7,V_b_8,T_a_6),V_z_46,T_a_6)
| ~ c_lessequals(c_0,V_z_46,T_a_6)
| ~ class_Orderings_Oorder(T_a_6)
| ~ c_lessequals(V_a_7,V_b_8,T_a_6)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_6) ),
inference(resolution,[status(thm)],[c_12,c_84]) ).
tff(c_1762,plain,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(splitRight,[status(thm)],[c_183]) ).
tff(c_2310,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_f(v_x),v_k(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(resolution,[status(thm)],[c_93,c_1762]) ).
tff(c_2340,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_44,c_196,c_67,c_1763,c_2310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA029-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % 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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 14:53:32 EDT 2025
% 0.14/0.34 % CPUTime :
% 4.88/2.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.88/2.20
% 4.88/2.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------