%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ANA035-2 : 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 : n012.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 3.72s 1.99s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ class_Ring__and__Field_Oordered__idom > class_OrderedGroup_Oab__semigroup__mult > c_times > c_HOL_Oabs > #nlpp > v_g > v_f > v_x > v_ca > v_c > t_b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_c,type,
v_c: $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $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(v_ca,type,
v_ca: $i ).
tff(v_g,type,
v_g: $i > $i ).
tff(v_f,type,
v_f: $i > $i ).
tff(t_b,type,
t_b: $i ).
tff(f_28,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_48,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [T_a,V_a,V_b] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a) ) ),
file(unknown,unknown) ).
tff(f_38,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| ( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_43,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ) ),
file(unknown,unknown) ).
tff(f_27,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(c_4,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_13,plain,
! [T_12] :
( class_OrderedGroup_Oab__semigroup__mult(T_12)
| ~ class_Ring__and__Field_Oordered__idom(T_12) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_17,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_18,plain,
! [V_b_13,V_a_14,T_a_15] :
( ( c_times(V_b_13,V_a_14,T_a_15) = c_times(V_a_14,V_b_13,T_a_15) )
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a_15) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_21,plain,
! [V_b_13,V_a_14] : ( c_times(V_b_13,V_a_14,t_b) = c_times(V_a_14,V_b_13,t_b) ),
inference(resolution,[status(thm)],[c_17,c_18]) ).
tff(c_221,plain,
! [V_b_25,V_a_26,V_c_27,T_a_28] :
( ( c_times(V_b_25,c_times(V_a_26,V_c_27,T_a_28),T_a_28) = c_times(V_a_26,c_times(V_b_25,V_c_27,T_a_28),T_a_28) )
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a_28) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_320,plain,
! [V_a_26,V_c_27,V_a_14] :
( ( c_times(c_times(V_a_26,V_c_27,t_b),V_a_14,t_b) = c_times(V_a_26,c_times(V_a_14,V_c_27,t_b),t_b) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_221]) ).
tff(c_373,plain,
! [V_a_26,V_c_27,V_a_14] : ( c_times(c_times(V_a_26,V_c_27,t_b),V_a_14,t_b) = c_times(V_a_26,c_times(V_a_14,V_c_27,t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_17,c_320]) ).
tff(c_55,plain,
! [V_a_18,T_a_19,V_b_20] :
( ( c_times(c_HOL_Oabs(V_a_18,T_a_19),c_HOL_Oabs(V_b_20,T_a_19),T_a_19) = c_HOL_Oabs(c_times(V_a_18,V_b_20,T_a_19),T_a_19) )
| ~ class_Ring__and__Field_Oordered__idom(T_a_19) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_62,plain,
! [V_b_20,V_a_18] :
( ( c_times(c_HOL_Oabs(V_b_20,t_b),c_HOL_Oabs(V_a_18,t_b),t_b) = c_HOL_Oabs(c_times(V_a_18,V_b_20,t_b),t_b) )
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_55,c_21]) ).
tff(c_80,plain,
! [V_b_20,V_a_18] : ( c_times(c_HOL_Oabs(V_b_20,t_b),c_HOL_Oabs(V_a_18,t_b),t_b) = c_HOL_Oabs(c_times(V_a_18,V_b_20,t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_62]) ).
tff(c_316,plain,
! [V_b_25,V_b_13,V_a_14] :
( ( c_times(V_b_25,c_times(V_b_13,V_a_14,t_b),t_b) = c_times(V_a_14,c_times(V_b_25,V_b_13,t_b),t_b) )
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_221]) ).
tff(c_371,plain,
! [V_b_25,V_b_13,V_a_14] : ( c_times(V_b_25,c_times(V_b_13,V_a_14,t_b),t_b) = c_times(V_a_14,c_times(V_b_25,V_b_13,t_b),t_b) ),
inference(demodulation,[status(thm),theory(equality)],[c_17,c_316]) ).
tff(c_2,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_27]) ).
tff(c_730,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_21,c_373,c_21,c_80,c_21,c_371,c_21,c_371,c_21,c_371,c_21,c_371,c_21,c_371,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ANA035-2 : 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
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 14:54:30 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.72/1.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.72/2.00
% 3.72/2.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------