%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA023-2 : 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 : n014.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 05:37:36 PM UTC 2025
% Result : Unsatisfiable 3.15s 1.83s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 82 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 81 ( 43 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Ocomm__monoid__add > c_plus > c_minus > #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_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
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(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_plus,type,
c_plus: ( $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_59,axiom,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
file(unknown,unknown) ).
tff(f_82,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_76,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [T] :
( ~ class_Orderings_Olinorder(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_57,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_58,axiom,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file(unknown,unknown) ).
tff(f_81,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__group__add(T) ),
file(unknown,unknown) ).
tff(f_71,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ),
file(unknown,unknown) ).
tff(f_30,axiom,
! [T_a,V_y] :
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ( c_plus(c_0,V_y,T_a) = V_y ) ),
file(unknown,unknown) ).
tff(f_38,axiom,
! [T_a,V_a,V_c,V_b] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_61,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file(unknown,unknown) ).
tff(c_12,plain,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_24,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_36,plain,
! [T_22] :
( class_Orderings_Olinorder(T_22)
| ~ class_Ring__and__Field_Oordered__idom(T_22) ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_40,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_24,c_36]) ).
tff(c_16,plain,
! [T_15] :
( class_Orderings_Oorder(T_15)
| ~ class_Orderings_Olinorder(T_15) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_54,plain,
! [V_x_26,V_z_27,T_a_28,V_y_29] :
( c_lessequals(V_x_26,V_z_27,T_a_28)
| ~ c_lessequals(V_x_26,V_y_29,T_a_28)
| ~ c_lessequals(V_y_29,V_z_27,T_a_28)
| ~ class_Orderings_Oorder(T_a_28) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_60,plain,
! [V_z_27] :
( c_lessequals(v_k(v_x),V_z_27,t_b)
| ~ c_lessequals(v_f(v_x),V_z_27,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_12,c_54]) ).
tff(c_61,plain,
~ class_Orderings_Oorder(t_b),
inference(splitLeft,[status(thm)],[c_60]) ).
tff(c_73,plain,
~ class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_16,c_61]) ).
tff(c_77,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_73]) ).
tff(c_79,plain,
class_Orderings_Oorder(t_b),
inference(splitRight,[status(thm)],[c_60]) ).
tff(c_10,plain,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_25,plain,
! [T_19] :
( class_OrderedGroup_Opordered__ab__group__add(T_19)
| ~ class_Ring__and__Field_Oordered__idom(T_19) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_29,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[c_24,c_25]) ).
tff(c_30,plain,
! [T_20] :
( class_OrderedGroup_Ocomm__monoid__add(T_20)
| ~ class_Ring__and__Field_Oordered__idom(T_20) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_34,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolution,[status(thm)],[c_24,c_30]) ).
tff(c_41,plain,
! [V_y_23,T_a_24] :
( ( c_plus(c_0,V_y_23,T_a_24) = V_y_23 )
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a_24) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_44,plain,
! [V_y_23] : ( c_plus(c_0,V_y_23,t_b) = V_y_23 ),
inference(resolution,[status(thm)],[c_34,c_41]) ).
tff(c_86,plain,
! [V_a_35,V_b_36,T_a_37,V_c_38] :
( c_lessequals(c_plus(V_a_35,V_b_36,T_a_37),V_c_38,T_a_37)
| ~ c_lessequals(V_a_35,c_minus(V_c_38,V_b_36,T_a_37),T_a_37)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_37) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_91,plain,
! [V_y_23,V_c_38] :
( c_lessequals(V_y_23,V_c_38,t_b)
| ~ c_lessequals(c_0,c_minus(V_c_38,V_y_23,t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_86]) ).
tff(c_95,plain,
! [V_y_39,V_c_40] :
( c_lessequals(V_y_39,V_c_40,t_b)
| ~ c_lessequals(c_0,c_minus(V_c_40,V_y_39,t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_91]) ).
tff(c_99,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(resolution,[status(thm)],[c_10,c_95]) ).
tff(c_8,plain,
! [V_x_14,V_z_13,T_a_11,V_y_12] :
( c_lessequals(V_x_14,V_z_13,T_a_11)
| ~ c_lessequals(V_x_14,V_y_12,T_a_11)
| ~ c_lessequals(V_y_12,V_z_13,T_a_11)
| ~ class_Orderings_Oorder(T_a_11) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_101,plain,
! [V_z_13] :
( c_lessequals(v_g(v_x),V_z_13,t_b)
| ~ c_lessequals(v_k(v_x),V_z_13,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_99,c_8]) ).
tff(c_105,plain,
! [V_z_41] :
( c_lessequals(v_g(v_x),V_z_41,t_b)
| ~ c_lessequals(v_k(v_x),V_z_41,t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_79,c_101]) ).
tff(c_113,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[status(thm)],[c_12,c_105]) ).
tff(c_125,plain,
! [V_a_43,V_c_44,V_b_45,T_a_46] :
( c_lessequals(V_a_43,c_minus(V_c_44,V_b_45,T_a_46),T_a_46)
| ~ c_lessequals(c_plus(V_a_43,V_b_45,T_a_46),V_c_44,T_a_46)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a_46) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_131,plain,
! [V_c_44,V_y_23] :
( c_lessequals(c_0,c_minus(V_c_44,V_y_23,t_b),t_b)
| ~ c_lessequals(V_y_23,V_c_44,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_125]) ).
tff(c_135,plain,
! [V_c_47,V_y_48] :
( c_lessequals(c_0,c_minus(V_c_47,V_y_48,t_b),t_b)
| ~ c_lessequals(V_y_48,V_c_47,t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_29,c_131]) ).
tff(c_14,plain,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_143,plain,
~ c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[status(thm)],[c_135,c_14]) ).
tff(c_151,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_113,c_143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA023-2 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % 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
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 14:52:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.15/1.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/1.84
% 3.15/1.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------