%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA039-2 : 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 : n018.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 05:37:39 PM UTC 2025
% Result : Unsatisfiable 4.75s 2.71s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 40 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Olordered__ab__group__abs > c_times > c_HOL_Oabs > #nlpp > v_h > v_f > v_x > v_c > t_a > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_c,type,
v_c: $i ).
tff(v_h,type,
v_h: $i > $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(t_a,type,
t_a: $i ).
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(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(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(v_f,type,
v_f: $i > $i ).
tff(f_30,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file(unknown,unknown) ).
tff(f_77,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file(unknown,unknown) ).
tff(f_40,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_35,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__semiring(T) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_Ring__and__Field_Opordered__semiring(T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Oorder(T) ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [V_U] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(f_51,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_29,axiom,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file(unknown,unknown) ).
tff(c_6,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_21,plain,
! [T_17] :
( class_OrderedGroup_Olordered__ab__group__abs(T_17)
| ~ class_Ring__and__Field_Oordered__idom(T_17) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_25,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_6,c_21]) ).
tff(c_10,plain,
! [V_a_5,T_a_4] :
( c_lessequals(c_0,c_HOL_Oabs(V_a_5,T_a_4),T_a_4)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a_4) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_8,plain,
! [V_a_3,T_a_2] :
( c_lessequals(V_a_3,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_35]) ).
tff(c_16,plain,
! [T_14] :
( class_Ring__and__Field_Opordered__semiring(T_14)
| ~ class_Ring__and__Field_Oordered__idom(T_14) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_14,plain,
! [V_a_11,V_c_13,T_a_10,V_b_12] :
( c_lessequals(c_times(V_a_11,V_c_13,T_a_10),c_times(V_b_12,V_c_13,T_a_10),T_a_10)
| ~ c_lessequals(c_0,V_c_13,T_a_10)
| ~ c_lessequals(V_a_11,V_b_12,T_a_10)
| ~ class_Ring__and__Field_Opordered__semiring(T_a_10) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_26,plain,
! [T_18] :
( class_Orderings_Oorder(T_18)
| ~ class_Ring__and__Field_Oordered__idom(T_18) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_30,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[c_6,c_26]) ).
tff(c_2,plain,
! [V_U_1] : c_lessequals(c_HOL_Oabs(v_h(V_U_1),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U_1),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_35,plain,
! [V_x_25,V_z_26,T_a_27,V_y_28] :
( c_lessequals(V_x_25,V_z_26,T_a_27)
| ~ c_lessequals(V_x_25,V_y_28,T_a_27)
| ~ c_lessequals(V_y_28,V_z_26,T_a_27)
| ~ class_Orderings_Oorder(T_a_27) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_37,plain,
! [V_U_1,V_z_26] :
( c_lessequals(c_HOL_Oabs(v_h(V_U_1),t_a),V_z_26,t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U_1),t_a),t_a),V_z_26,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(resolution,[status(thm)],[c_2,c_35]) ).
tff(c_209,plain,
! [V_U_56,V_z_57] :
( c_lessequals(c_HOL_Oabs(v_h(V_U_56),t_a),V_z_57,t_a)
| ~ c_lessequals(c_times(v_c,c_HOL_Oabs(v_f(V_U_56),t_a),t_a),V_z_57,t_a) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_37]) ).
tff(c_226,plain,
! [V_U_56,V_b_12] :
( c_lessequals(c_HOL_Oabs(v_h(V_U_56),t_a),c_times(V_b_12,c_HOL_Oabs(v_f(V_U_56),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(V_U_56),t_a),t_a)
| ~ c_lessequals(v_c,V_b_12,t_a)
| ~ class_Ring__and__Field_Opordered__semiring(t_a) ),
inference(resolution,[status(thm)],[c_14,c_209]) ).
tff(c_592,plain,
~ class_Ring__and__Field_Opordered__semiring(t_a),
inference(splitLeft,[status(thm)],[c_226]) ).
tff(c_595,plain,
~ class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[status(thm)],[c_16,c_592]) ).
tff(c_599,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_595]) ).
tff(c_726,plain,
! [V_U_95,V_b_96] :
( c_lessequals(c_HOL_Oabs(v_h(V_U_95),t_a),c_times(V_b_96,c_HOL_Oabs(v_f(V_U_95),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(V_U_95),t_a),t_a)
| ~ c_lessequals(v_c,V_b_96,t_a) ),
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_4,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_738,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a)
| ~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a) ),
inference(resolution,[status(thm)],[c_726,c_4]) ).
tff(c_748,plain,
~ c_lessequals(v_c,c_HOL_Oabs(v_c,t_a),t_a),
inference(splitLeft,[status(thm)],[c_738]) ).
tff(c_751,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_8,c_748]) ).
tff(c_755,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25,c_751]) ).
tff(c_756,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_a),t_a),
inference(splitRight,[status(thm)],[c_738]) ).
tff(c_866,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c_10,c_756]) ).
tff(c_870,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25,c_866]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA039-2 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.09 % 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
% 0.09/0.29 % Computer : n018.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Apr 7 14:54:47 EDT 2025
% 0.09/0.29 % CPUTime :
% 4.75/2.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/2.72
% 4.75/2.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------