TSTP Solution File: ANA028-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ANA028-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 Aug 30 17:13:59 EDT 2023
% Result : Unsatisfiable 0.19s 0.78s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 26
% Syntax : Number of formulae : 67 ( 28 unt; 13 typ; 0 def)
% Number of atoms : 89 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 39 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_23,type,
c_0: $i ).
tff(decl_24,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_26,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_28,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
v_g: $i > $i ).
tff(decl_30,type,
v_k: $i > $i ).
tff(decl_31,type,
t_b: $i ).
tff(decl_32,type,
v_x: $i ).
tff(decl_33,type,
v_f: $i > $i ).
tff(decl_34,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( c_plus(c_0,X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
cnf(cls_OrderedGroup_Ocompare__rls__5_0,axiom,
( c_minus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__5_0) ).
cnf(cls_OrderedGroup_Odiff__self_0,axiom,
( c_minus(X2,X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__3_0,axiom,
( c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_1,axiom,
( c_lessequals(c_minus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_plus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
cnf(cls_OrderedGroup_Ocompare__rls__2_0,axiom,
( c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( c_lessequals(X2,c_minus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_54,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
cnf(c_0_13,axiom,
( c_plus(c_0,X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 ).
cnf(c_0_14,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_23 ).
cnf(c_0_15,plain,
( c_plus(c_0,X1,X2) = X1
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_17,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_4 ).
cnf(c_0_18,axiom,
( c_minus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__5_0 ).
cnf(c_0_19,negated_conjecture,
c_plus(c_0,X1,t_b) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
class_OrderedGroup_Oab__group__add(t_b),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,axiom,
( c_minus(X2,X2,X1) = c_0
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Odiff__self_0 ).
cnf(c_0_22,negated_conjecture,
c_minus(c_0,c_minus(X1,X2,t_b),t_b) = c_minus(X2,X1,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,axiom,
( c_plus(c_minus(X2,X3,X1),X4,X1) = c_minus(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__3_0 ).
cnf(c_0_24,negated_conjecture,
c_minus(X1,X1,t_b) = c_0,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
c_minus(c_minus(X1,X2,t_b),c_0,t_b) = c_minus(X1,X2,t_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_22]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
c_minus(c_plus(X1,X2,t_b),X1,t_b) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
c_minus(X1,c_0,t_b) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,negated_conjecture,
c_minus(X1,c_minus(c_0,X2,t_b),t_b) = c_plus(X1,X2,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_27]),c_0_20])]) ).
cnf(c_0_29,negated_conjecture,
c_minus(X1,c_plus(X2,X3,t_b),t_b) = c_minus(c_minus(X1,X3,t_b),X2,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_22]),c_0_20])]) ).
cnf(c_0_30,negated_conjecture,
c_plus(c_minus(c_0,X1,t_b),X1,t_b) = c_0,
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
c_minus(X1,c_minus(X1,X2,t_b),t_b) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_26]),c_0_20])]) ).
cnf(c_0_32,negated_conjecture,
c_plus(c_minus(X1,X2,t_b),X2,t_b) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]),c_0_28]) ).
cnf(c_0_33,negated_conjecture,
c_minus(c_plus(X1,X2,t_b),X2,t_b) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_34,axiom,
( c_lessequals(c_minus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_plus(X3,X4,X1),X1) ),
cls_OrderedGroup_Ocompare__rls__8_1 ).
cnf(c_0_35,negated_conjecture,
c_plus(X1,X2,t_b) = c_plus(X2,X1,t_b),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
c_minus(c_plus(X1,X2,t_b),X3,t_b) = c_minus(X1,c_minus(X3,X2,t_b),t_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_22]) ).
cnf(c_0_37,axiom,
( c_plus(X2,c_minus(X3,X4,X1),X1) = c_minus(c_plus(X2,X3,X1),X4,X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_OrderedGroup_Ocompare__rls__2_0 ).
cnf(c_0_38,negated_conjecture,
c_plus(X1,c_0,t_b) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( c_lessequals(c_minus(X1,X2,t_b),X3,t_b)
| ~ c_lessequals(X1,c_plus(X2,X3,t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,axiom,
( c_lessequals(X2,c_minus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),X4,X1) ),
cls_OrderedGroup_Ocompare__rls__9_1 ).
cnf(c_0_41,negated_conjecture,
c_minus(X1,c_minus(c_minus(X1,X2,t_b),X3,t_b),t_b) = c_plus(X2,X3,t_b),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_31]),c_0_20])]),c_0_36]) ).
cnf(c_0_42,negated_conjecture,
c_plus(c_minus(X1,X2,t_b),X3,t_b) = c_minus(X3,c_minus(X2,X1,t_b),t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_19]),c_0_20])]) ).
cnf(c_0_43,negated_conjecture,
c_plus(X1,c_minus(X2,X3,t_b),t_b) = c_minus(X1,c_minus(X3,X2,t_b),t_b),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_20])]),c_0_38]) ).
cnf(c_0_44,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_45,negated_conjecture,
( c_lessequals(c_minus(X1,X2,t_b),c_minus(X3,X4,t_b),t_b)
| ~ c_lessequals(X1,c_minus(X2,c_minus(X4,X3,t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_20])]),c_0_36]) ).
cnf(c_0_46,plain,
( c_lessequals(X1,c_minus(X2,c_minus(X3,X4,X5),X5),X5)
| ~ c_lessequals(c_minus(c_plus(X1,X3,X5),X4,X5),X2,X5)
| ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_OrderedGroup_Oab__group__add(X5) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_47,negated_conjecture,
c_minus(X1,c_minus(X2,c_minus(X3,X1,t_b),t_b),t_b) = c_minus(X3,X2,t_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_28]),c_0_42]),c_0_43]),c_0_27]) ).
cnf(c_0_48,negated_conjecture,
( ~ c_lessequals(v_f(v_x),c_minus(v_k(v_x),c_minus(v_g(v_x),v_f(v_x),t_b),t_b),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( c_lessequals(X1,c_minus(X2,c_minus(X3,X1,t_b),t_b),t_b)
| ~ c_lessequals(X3,X2,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_20])]),c_0_36]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
c_lessequals(v_g(X1),v_k(X1),t_b),
cls_conjecture_1 ).
cnf(c_0_51,negated_conjecture,
~ class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_52,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_54 ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA028-2 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 18:13:30 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.78 % Version : CSE_E---1.5
% 0.19/0.78 % Problem : theBenchmark.p
% 0.19/0.78 % Proof found
% 0.19/0.78 % SZS status Theorem for theBenchmark.p
% 0.19/0.78 % SZS output start Proof
% See solution above
% 0.19/0.79 % Total time : 0.205000 s
% 0.19/0.79 % SZS output end Proof
% 0.19/0.79 % Total time : 0.208000 s
%------------------------------------------------------------------------------