%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA009-2 : 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 : n006.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 05:37:32 PM UTC 2025
% Result : Unsatisfiable 2.53s 1.60s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 21 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Oab__group__add > c_plus > c_uminus > #nlpp > v_lb > v_f > v_x > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_lb,type,
v_lb: $i > $i ).
tff(c_0,type,
c_0: $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $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(c_plus,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_uminus,type,
c_uminus: ( $i * $i ) > $i ).
tff(v_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(f_53,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_52,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__group__add(T) ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [V_U] : c_lessequals(v_lb(V_U),v_f(V_U),t_b),
file(unknown,unknown) ).
tff(f_38,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Oab__group__add(T_a)
| ( c_plus(V_a,c_uminus(V_a,T_a),T_a) = c_0 ) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_42,axiom,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(c_14,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_15,plain,
! [T_10] :
( class_OrderedGroup_Oab__group__add(T_10)
| ~ class_Ring__and__Field_Oordered__idom(T_10) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_19,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[status(thm)],[c_14,c_15]) ).
tff(c_20,plain,
! [T_11] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_11)
| ~ class_Ring__and__Field_Oordered__idom(T_11) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_24,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(resolution,[status(thm)],[c_14,c_20]) ).
tff(c_6,plain,
! [V_U_7] : c_lessequals(v_lb(V_U_7),v_f(V_U_7),t_b),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_4,plain,
! [V_a_6,T_a_5] :
( ( c_plus(V_a_6,c_uminus(V_a_6,T_a_5),T_a_5) = c_0 )
| ~ class_OrderedGroup_Oab__group__add(T_a_5) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_35,plain,
! [V_a_15,V_c_16,T_a_17,V_b_18] :
( c_lessequals(c_plus(V_a_15,V_c_16,T_a_17),c_plus(V_b_18,V_c_16,T_a_17),T_a_17)
| ~ c_lessequals(V_a_15,V_b_18,T_a_17)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a_17) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_42,plain,
! [V_b_19,V_a_20,T_a_21] :
( c_lessequals(c_0,c_plus(V_b_19,c_uminus(V_a_20,T_a_21),T_a_21),T_a_21)
| ~ c_lessequals(V_a_20,V_b_19,T_a_21)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a_21)
| ~ class_OrderedGroup_Oab__group__add(T_a_21) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_35]) ).
tff(c_8,plain,
~ c_lessequals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_45,plain,
( ~ c_lessequals(v_lb(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) ),
inference(resolution,[status(thm)],[c_42,c_8]) ).
tff(c_52,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_19,c_24,c_6,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA009-2 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Apr 7 14:49:53 EDT 2025
% 0.12/0.32 % CPUTime :
% 2.53/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.53/1.60
% 2.53/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------