%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA034-10 : TPTP v9.0.0. Released v7.3.0.
% 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 : 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 05:37:38 PM UTC 2025
% Result : Unsatisfiable 6.19s 2.50s
% Output : CNFRefutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 57 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 66 ( 66 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ifeq2 > ifeq > c_times > c_lessequals > c_less > c_HOL_Oabs > #nlpp > v_g > v_f > v_b > v_a > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__idom > class_Orderings_Oorder > class_OrderedGroup_Olordered__ab__group__abs > v_x > v_ca > v_c > true > t_b > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $i ).
tff(v_c,type,
v_c: $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $i ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(c_less,type,
c_less: ( $i * $i * $i ) > $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $i ).
tff(v_a,type,
v_a: $i > $i ).
tff(c_0,type,
c_0: $i ).
tff(ifeq2,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(c_times,type,
c_times: ( $i * $i * $i ) > $i ).
tff(v_b,type,
v_b: $i > $i ).
tff(v_ca,type,
v_ca: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $i ).
tff(true,type,
true: $i ).
tff(v_g,type,
v_g: $i > $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $i ).
tff(v_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(ifeq,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(f_42,axiom,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
file(unknown,unknown) ).
tff(f_26,axiom,
! [A,B,C] : ( ifeq(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_43,axiom,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file(unknown,unknown) ).
tff(f_51,axiom,
! [T] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [T_a,V_a] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [T] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true ),
file(unknown,unknown) ).
tff(f_45,axiom,
! [T] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true ),
file(unknown,unknown) ).
tff(f_37,axiom,
c_less(c_0,v_c,t_b) = true,
file(unknown,unknown) ).
tff(f_34,axiom,
! [V_x,V_y,T_a] : ( ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true ),
file(unknown,unknown) ).
tff(f_32,axiom,
! [T_a,V_a,V_b] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true ),
file(unknown,unknown) ).
tff(f_40,axiom,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(f_28,axiom,
! [T_a,V_a,V_b] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [A,B,C] : ( ifeq2(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_38,axiom,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
file(unknown,unknown) ).
tff(f_49,axiom,
! [T] : ( ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true ),
file(unknown,unknown) ).
tff(f_39,axiom,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
file(unknown,unknown) ).
tff(f_30,axiom,
! [V_a,T_a,V_d,V_c,V_b] : ( ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true ),
file(unknown,unknown) ).
tff(c_24,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_4,plain,
! [A_4,B_5,C_6] : ( ifeq(A_4,A_4,B_5,C_6) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_26,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_68,plain,
! [T_34] : ( ifeq(class_Ring__and__Field_Oordered__idom(T_34),true,class_OrderedGroup_Olordered__ab__group__abs(T_34),true) = true ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_75,plain,
ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_26,c_68]) ).
tff(c_81,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(superposition,[status(thm),theory(equality)],[c_75,c_4]) ).
tff(c_184,plain,
! [T_a_37,V_a_38] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a_37),true,c_lessequals(c_0,c_HOL_Oabs(V_a_38,T_a_37),T_a_37),true) = true ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_195,plain,
! [V_a_39] : ( ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(V_a_39,t_b),t_b),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_81,c_184]) ).
tff(c_200,plain,
! [V_a_39] : ( c_lessequals(c_0,c_HOL_Oabs(V_a_39,t_b),t_b) = true ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_4]) ).
tff(c_153,plain,
! [T_36] : ( ifeq(class_Ring__and__Field_Oordered__idom(T_36),true,class_Ring__and__Field_Opordered__cancel__semiring(T_36),true) = true ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_160,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_26,c_153]) ).
tff(c_167,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(superposition,[status(thm),theory(equality)],[c_160,c_4]) ).
tff(c_28,plain,
! [T_23] : ( ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_23),true,class_Orderings_Oorder(T_23),true) = true ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_96,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_81,c_28]) ).
tff(c_136,plain,
class_Orderings_Oorder(t_b) = true,
inference(superposition,[status(thm),theory(equality)],[c_96,c_4]) ).
tff(c_16,plain,
c_less(c_0,v_c,t_b) = true,
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_230,plain,
! [V_x_41,V_y_42,T_a_43] : ( ifeq(c_less(V_x_41,V_y_42,T_a_43),true,ifeq(class_Orderings_Oorder(T_a_43),true,c_lessequals(V_x_41,V_y_42,T_a_43),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_249,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_16,c_230]) ).
tff(c_256,plain,
c_lessequals(c_0,v_c,t_b) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_136,c_249]) ).
tff(c_354,plain,
! [T_a_54,V_a_55,V_b_56] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a_54),true,ifeq(c_lessequals(c_0,V_a_55,T_a_54),true,ifeq(c_lessequals(c_0,V_b_56,T_a_54),true,c_lessequals(c_0,c_times(V_a_55,V_b_56,T_a_54),T_a_54),true),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_364,plain,
! [V_b_56] : ( ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(true,true,ifeq(c_lessequals(c_0,V_b_56,t_b),true,c_lessequals(c_0,c_times(v_c,V_b_56,t_b),t_b),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_256,c_354]) ).
tff(c_384,plain,
! [V_b_57] : ( ifeq(c_lessequals(c_0,V_b_57,t_b),true,c_lessequals(c_0,c_times(v_c,V_b_57,t_b),t_b),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_167,c_4,c_364]) ).
tff(c_461,plain,
! [V_a_58] : ( ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(V_a_58,t_b),t_b),t_b),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_200,c_384]) ).
tff(c_466,plain,
! [V_a_58] : ( c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(V_a_58,t_b),t_b),t_b) = true ),
inference(superposition,[status(thm),theory(equality)],[c_461,c_4]) ).
tff(c_22,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_272,plain,
! [T_a_45,V_a_46,V_b_47] : ( ifeq2(class_Ring__and__Field_Oordered__idom(T_a_45),true,c_times(c_HOL_Oabs(V_a_46,T_a_45),c_HOL_Oabs(V_b_47,T_a_45),T_a_45),c_HOL_Oabs(c_times(V_a_46,V_b_47,T_a_45),T_a_45)) = c_HOL_Oabs(c_times(V_a_46,V_b_47,T_a_45),T_a_45) ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_319,plain,
! [V_a_50,V_b_51] : ( ifeq2(true,true,c_times(c_HOL_Oabs(V_a_50,t_b),c_HOL_Oabs(V_b_51,t_b),t_b),c_HOL_Oabs(c_times(V_a_50,V_b_51,t_b),t_b)) = c_HOL_Oabs(c_times(V_a_50,V_b_51,t_b),t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_272]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( ifeq2(A_1,A_1,B_2,C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_325,plain,
! [V_a_50,V_b_51] : ( c_times(c_HOL_Oabs(V_a_50,t_b),c_HOL_Oabs(V_b_51,t_b),t_b) = c_HOL_Oabs(c_times(V_a_50,V_b_51,t_b),t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_319,c_2]) ).
tff(c_18,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_102,plain,
! [T_35] : ( ifeq(class_Ring__and__Field_Oordered__idom(T_35),true,class_Ring__and__Field_Opordered__semiring(T_35),true) = true ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_109,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_26,c_102]) ).
tff(c_115,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(superposition,[status(thm),theory(equality)],[c_109,c_4]) ).
tff(c_20,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_509,plain,
! [V_d_64,T_a_60,V_c_62,V_b_63,V_a_61] : ( ifeq(c_lessequals(c_0,V_b_63,T_a_60),true,ifeq(c_lessequals(c_0,V_c_62,T_a_60),true,ifeq(c_lessequals(V_a_61,V_b_63,T_a_60),true,ifeq(c_lessequals(V_c_62,V_d_64,T_a_60),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a_60),true,c_lessequals(c_times(V_a_61,V_c_62,T_a_60),c_times(V_b_63,V_d_64,T_a_60),T_a_60),true),true),true),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_573,plain,
! [V_b_63,V_a_61] : ( ifeq(c_lessequals(c_0,V_b_63,t_b),true,ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(c_lessequals(V_a_61,V_b_63,t_b),true,ifeq(true,true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(V_a_61,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(V_b_63,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true),true),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_509]) ).
tff(c_2335,plain,
! [V_b_107,V_a_108] : ( ifeq(c_lessequals(c_0,V_b_107,t_b),true,ifeq(c_lessequals(V_a_108,V_b_107,t_b),true,c_lessequals(c_times(V_a_108,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(V_b_107,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_200,c_4,c_115,c_4,c_573]) ).
tff(c_2421,plain,
ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(true,true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_18,c_2335]) ).
tff(c_2446,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_466,c_22,c_325,c_4,c_2421]) ).
tff(c_2448,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_24,c_2446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA034-10 : TPTP v9.0.0. Released v7.3.0.
% 0.06/0.12 % 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
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Apr 7 14:54:35 EDT 2025
% 0.13/0.34 % CPUTime :
% 6.19/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.19/2.51
% 6.19/2.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------