%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA016-2 : 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 : n014.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 05:37:34 PM UTC 2025
% Result : Unsatisfiable 2.96s 1.71s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Ofield > class_OrderedGroup_Osemigroup__mult > class_OrderedGroup_Omonoid__mult > c_times > c_HOL_Oinverse > #nlpp > v_g > v_x > v_c > t_a > c_1 > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_c,type,
v_c: $i ).
tff(t_a,type,
t_a: $i ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
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_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_g,type,
v_g: $i > $i ).
tff(f_27,axiom,
v_c != c_0,
file(unknown,unknown) ).
tff(f_30,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file(unknown,unknown) ).
tff(f_62,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ),
file(unknown,unknown) ).
tff(f_35,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_47,axiom,
! [T_a,V_a] :
( ~ class_Ring__and__Field_Ofield(T_a)
| ( V_a = c_0 )
| ( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1 ) ),
file(unknown,unknown) ).
tff(f_40,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_29,axiom,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file(unknown,unknown) ).
tff(c_2,plain,
v_c != c_0,
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_6,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_21,plain,
! [T_14] :
( class_Ring__and__Field_Ofield(T_14)
| ~ class_Ring__and__Field_Oordered__field(T_14) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_25,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[c_6,c_21]) ).
tff(c_16,plain,
! [T_10] :
( class_OrderedGroup_Osemigroup__mult(T_10)
| ~ class_Ring__and__Field_Ofield(T_10) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_34,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[status(thm)],[c_25,c_16]) ).
tff(c_14,plain,
! [T_9] :
( class_OrderedGroup_Omonoid__mult(T_9)
| ~ class_Ring__and__Field_Ofield(T_9) ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_33,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolution,[status(thm)],[c_25,c_14]) ).
tff(c_8,plain,
! [V_y_2,T_a_1] :
( ( c_times(c_1,V_y_2,T_a_1) = V_y_2 )
| ~ class_OrderedGroup_Omonoid__mult(T_a_1) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_37,plain,
! [V_y_2] : ( c_times(c_1,V_y_2,t_a) = V_y_2 ),
inference(resolution,[status(thm)],[c_33,c_8]) ).
tff(c_12,plain,
! [V_a_8,T_a_7] :
( ( c_times(V_a_8,c_HOL_Oinverse(V_a_8,T_a_7),T_a_7) = c_1 )
| ( c_0 = V_a_8 )
| ~ class_Ring__and__Field_Ofield(T_a_7) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_208,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_40]) ).
tff(c_240,plain,
! [V_a_36,T_a_37,V_c_38] :
( ( c_times(V_a_36,c_times(c_HOL_Oinverse(V_a_36,T_a_37),V_c_38,T_a_37),T_a_37) = c_times(c_1,V_c_38,T_a_37) )
| ~ class_OrderedGroup_Osemigroup__mult(T_a_37)
| ( c_0 = V_a_36 )
| ~ class_Ring__and__Field_Ofield(T_a_37) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_208]) ).
tff(c_4,plain,
c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) != v_g(v_x),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_257,plain,
( ( c_times(c_1,v_g(v_x),t_a) != v_g(v_x) )
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ( v_c = c_0 )
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(superposition,[status(thm),theory(equality)],[c_240,c_4]) ).
tff(c_286,plain,
v_c = c_0,
inference(demodulation,[status(thm),theory(equality)],[c_25,c_34,c_37,c_257]) ).
tff(c_288,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2,c_286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA016-2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % 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
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 14:51:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.96/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.96/1.72
% 2.96/1.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------