%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA045-2 : 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 : n015.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 05:37:40 PM UTC 2025
% Result : Unsatisfiable 2.40s 1.48s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Oordered__idom > class_OrderedGroup_Olordered__ab__group__abs > c_times > c_HOL_Oabs > #nlpp > v_x > v_g > t_b > c_1 > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $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_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(v_g,type,
v_g: $i > $i ).
tff(v_x,type,
v_x: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(f_29,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_44,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_34,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_39,axiom,
! [T_a,V_c] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( V_c = c_times(c_1,V_c,T_a) ) ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [V_U] : ~ c_lessequals(c_0,c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(c_4,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_11,plain,
! [T_7] :
( class_OrderedGroup_Olordered__ab__group__abs(T_7)
| ~ class_Ring__and__Field_Oordered__idom(T_7) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_15,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_4,c_11]) ).
tff(c_6,plain,
! [V_a_3,T_a_2] :
( c_lessequals(c_0,c_HOL_Oabs(V_a_3,T_a_2),T_a_2)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_2) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_16,plain,
! [V_c_8,T_a_9] :
( ( c_times(c_1,V_c_8,T_a_9) = V_c_8 )
| ~ class_Ring__and__Field_Oordered__idom(T_a_9) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_19,plain,
! [V_c_8] : ( c_times(c_1,V_c_8,t_b) = V_c_8 ),
inference(resolution,[status(thm)],[c_4,c_16]) ).
tff(c_30,plain,
! [V_U_13] : ~ c_lessequals(c_0,c_times(V_U_13,c_HOL_Oabs(v_g(v_x(V_U_13)),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_34,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_g(v_x(c_1)),t_b),t_b),
inference(superposition,[status(thm),theory(equality)],[c_19,c_30]) ).
tff(c_37,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[c_6,c_34]) ).
tff(c_41,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : ANA045-2 : TPTP v9.0.0. Released v3.2.0.
% 0.02/0.09 % 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
% 0.08/0.29 % Computer : n015.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Apr 7 14:55:50 EDT 2025
% 0.08/0.29 % CPUTime :
% 2.40/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.40/1.48
% 2.40/1.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------