TSTP Solution File: SWV886-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV886-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 : Thu Aug 31 21:48:31 EDT 2023
% Result : Unsatisfiable 0.50s 0.76s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 75
% Syntax : Number of formulae : 95 ( 24 unt; 64 typ; 0 def)
% Number of atoms : 42 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 87 ( 55 >; 32 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 1 prp; 0-4 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 34 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_25,type,
tc_bool: $i ).
tff(decl_26,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_27,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_29,type,
hBOOL: $i > $o ).
tff(decl_30,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
tc_nat: $i ).
tff(decl_32,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_34,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_35,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_38,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_39,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_40,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_41,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_42,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_43,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_44,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(decl_45,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_47,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_48,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_49,type,
c_Suc: $i > $i ).
tff(decl_50,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_52,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_53,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_54,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_55,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_56,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_57,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_58,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(decl_59,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_60,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_61,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_62,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_63,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_64,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_65,type,
class_Orderings_Obot: $i > $o ).
tff(decl_66,type,
class_HOL_Oord: $i > $o ).
tff(decl_67,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(decl_68,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_69,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_70,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_71,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_73,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_75,type,
c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1: ( $i * $i ) > $i ).
tff(decl_76,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(decl_77,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_78,type,
v_U: $i ).
tff(decl_79,type,
tc_Com_Opname: $i ).
tff(decl_80,type,
v_na: $i ).
tff(decl_81,type,
v_mgt__call: $i ).
tff(decl_82,type,
t_a: $i ).
tff(decl_83,type,
v_G: $i ).
tff(decl_84,type,
v_pn: $i ).
tff(decl_85,type,
c_fequal: ( $i * $i * $i ) > $o ).
cnf(cls_le__imp__diff__is__add_0,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
cnf(cls_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_card__insert__if_1,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| c_in(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
cnf(cls_conjecture_6,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_diff__add__inverse_0,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(cls_conjecture_5,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(c_0_11,axiom,
( X2 = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__imp__diff__is__add_0 ).
cnf(c_0_12,axiom,
c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),
cls_nat__add__commute_0 ).
cnf(c_0_13,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
cls_conjecture_2 ).
cnf(c_0_14,axiom,
c_Suc(X1) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
cls_Suc__eq__plus1_0 ).
cnf(c_0_15,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(X1),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X2),tc_nat),
cls_add__Suc__shift_0 ).
cnf(c_0_16,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
cls_conjecture_1 ).
cnf(c_0_17,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14]),c_0_14]) ).
cnf(c_0_20,negated_conjecture,
c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(rw,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_21,axiom,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_Suc(c_Finite__Set_Ocard(X2,X3))
| c_in(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
cls_card__insert__if_1 ).
cnf(c_0_22,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
cls_conjecture_6 ).
cnf(c_0_23,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a) = c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),tc_nat),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]),c_0_12]) ).
cnf(c_0_24,axiom,
c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat) = X2,
cls_diff__add__inverse_0 ).
cnf(c_0_25,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X2,X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_in(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(rw,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
( c_Finite__Set_Ocard(c_Set_Oinsert(X1,X2,X3),X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X2,X3),tc_nat)
| c_in(X1,X2,X3)
| ~ c_Finite__Set_Ofinite(X2,X3) ),
inference(rw,[status(thm)],[c_0_25,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
cls_conjecture_5 ).
cnf(c_0_29,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
cls_conjecture_4 ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV886-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n028.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 : Tue Aug 29 08:20:40 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.50/0.76 % Version : CSE_E---1.5
% 0.50/0.76 % Problem : theBenchmark.p
% 0.50/0.76 % Proof found
% 0.50/0.76 % SZS status Theorem for theBenchmark.p
% 0.50/0.76 % SZS output start Proof
% See solution above
% 0.50/0.76 % Total time : 0.189000 s
% 0.50/0.76 % SZS output end Proof
% 0.50/0.76 % Total time : 0.205000 s
%------------------------------------------------------------------------------