%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA014-2 : 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/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 : n027.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 05:37:33 PM UTC 2025
% Result : Unsatisfiable 3.83s 2.03s
% Output : CNFRefutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 43 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Ofield > class_Orderings_Oorder > class_OrderedGroup_Osemigroup__mult > class_OrderedGroup_Omonoid__mult > c_times > c_HOL_Oinverse > c_HOL_Oabs > #nlpp > v_x > v_f > v_c > t_a > c_1 > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_c,type,
v_c: $i ).
tff(t_a,type,
t_a: $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
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_1,type,
c_1: $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(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(v_x,type,
v_x: $i > $i ).
tff(v_f,type,
v_f: $i > $i ).
tff(f_31,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file(unknown,unknown) ).
tff(f_83,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_46,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_27,axiom,
v_c != c_0,
file(unknown,unknown) ).
tff(f_73,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [T_a,V_y] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_times(c_1,V_y,T_a) = V_y ) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [T_a,V_a] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ) ),
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(f_78,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Oordered__idom(T) ),
file(unknown,unknown) ).
tff(f_51,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_30,axiom,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(c_6,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_27,plain,
! [T_20] :
( class_Orderings_Oorder(T_20)
| ~ class_Ring__and__Field_Oordered__field(T_20) ),
inference(cnfTransformation,[status(thm)],[f_83]) ).
tff(c_31,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[c_6,c_27]) ).
tff(c_12,plain,
! [V_x_9,T_a_8] :
( c_lessequals(V_x_9,V_x_9,T_a_8)
| ~ class_Orderings_Oorder(T_a_8) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_2,plain,
v_c != c_0,
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_35,plain,
! [T_24] :
( class_Ring__and__Field_Ofield(T_24)
| ~ class_Ring__and__Field_Oordered__field(T_24) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_39,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[c_6,c_35]) ).
tff(c_20,plain,
! [T_16] :
( class_OrderedGroup_Osemigroup__mult(T_16)
| ~ class_Ring__and__Field_Ofield(T_16) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_46,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[status(thm)],[c_39,c_20]) ).
tff(c_18,plain,
! [T_15] :
( class_OrderedGroup_Omonoid__mult(T_15)
| ~ class_Ring__and__Field_Ofield(T_15) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_47,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolution,[status(thm)],[c_39,c_18]) ).
tff(c_49,plain,
! [V_y_27,T_a_28] :
( ( c_times(c_1,V_y_27,T_a_28) = V_y_27 )
| ~ class_OrderedGroup_Omonoid__mult(T_a_28) ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_52,plain,
! [V_y_27] : ( c_times(c_1,V_y_27,t_a) = V_y_27 ),
inference(resolution,[status(thm)],[c_47,c_49]) ).
tff(c_16,plain,
! [V_a_14,T_a_13] :
( ( c_times(c_HOL_Oinverse(V_a_14,T_a_13),V_a_14,T_a_13) = c_1 )
| ( c_0 = V_a_14 )
| ~ class_Ring__and__Field_Ofield(T_a_13) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_72,plain,
! [V_a_32,V_b_33,T_a_34,V_c_35] :
( ( c_times(c_times(V_a_32,V_b_33,T_a_34),V_c_35,T_a_34) = c_times(V_a_32,c_times(V_b_33,V_c_35,T_a_34),T_a_34) )
| ~ class_OrderedGroup_Osemigroup__mult(T_a_34) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_87,plain,
! [V_a_14,T_a_13,V_c_35] :
( ( c_times(c_HOL_Oinverse(V_a_14,T_a_13),c_times(V_a_14,V_c_35,T_a_13),T_a_13) = c_times(c_1,V_c_35,T_a_13) )
| ~ class_OrderedGroup_Osemigroup__mult(T_a_13)
| ( c_0 = V_a_14 )
| ~ class_Ring__and__Field_Ofield(T_a_13) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_72]) ).
tff(c_24,plain,
! [T_18] :
( class_Ring__and__Field_Oordered__idom(T_18)
| ~ class_Ring__and__Field_Oordered__field(T_18) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_14,plain,
! [V_a_11,T_a_10,V_b_12] :
( ( c_times(c_HOL_Oabs(V_a_11,T_a_10),c_HOL_Oabs(V_b_12,T_a_10),T_a_10) = c_HOL_Oabs(c_times(V_a_11,V_b_12,T_a_10),T_a_10) )
| ~ class_Ring__and__Field_Oordered__idom(T_a_10) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_720,plain,
! [V_U_66] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U_66)),t_a),c_times(V_U_66,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U_66)),t_a),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_739,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(c_1)),t_a),t_a),t_a),
inference(superposition,[status(thm),theory(equality)],[c_52,c_720]) ).
tff(c_748,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_1)),t_a),c_HOL_Oabs(c_times(v_c,v_f(v_x(c_1)),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_739]) ).
tff(c_749,plain,
~ class_Ring__and__Field_Oordered__idom(t_a),
inference(splitLeft,[status(thm)],[c_748]) ).
tff(c_752,plain,
~ class_Ring__and__Field_Oordered__field(t_a),
inference(resolution,[status(thm)],[c_24,c_749]) ).
tff(c_756,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_752]) ).
tff(c_758,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(splitRight,[status(thm)],[c_748]) ).
tff(c_731,plain,
! [V_U_66] :
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U_66)),t_a),c_times(V_U_66,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U_66)),t_a),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_720]) ).
tff(c_766,plain,
! [V_U_67] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U_67)),t_a),c_times(V_U_67,c_HOL_Oabs(c_times(v_c,v_f(v_x(V_U_67)),t_a),t_a),t_a),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_758,c_731]) ).
tff(c_774,plain,
! [V_a_11] :
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(V_a_11,t_a))),t_a),c_HOL_Oabs(c_times(V_a_11,c_times(v_c,v_f(v_x(c_HOL_Oabs(V_a_11,t_a))),t_a),t_a),t_a),t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_14,c_766]) ).
tff(c_787,plain,
! [V_a_68] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(V_a_68,t_a))),t_a),c_HOL_Oabs(c_times(V_a_68,c_times(v_c,v_f(v_x(c_HOL_Oabs(V_a_68,t_a))),t_a),t_a),t_a),t_a),
inference(demodulation,[status(thm),theory(equality)],[c_758,c_774]) ).
tff(c_795,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(c_times(c_1,v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a),t_a)
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( v_c = c_0 )
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_87,c_787]) ).
tff(c_805,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(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)
| ( v_c = c_0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_39,c_46,c_52,c_795]) ).
tff(c_806,plain,
~ c_lessequals(c_HOL_Oabs(v_f(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),
inference(negUnitSimplification,[status(thm)],[c_2,c_805]) ).
tff(c_811,plain,
~ class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[c_12,c_806]) ).
tff(c_815,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_31,c_811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA014-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 14:50:50 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.83/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/2.04
% 3.83/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------