TSTP Solution File: SWW473+5 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 : Fri Sep 1 00:18:03 EDT 2023
% Result : Theorem 0.67s 0.83s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 54
% Syntax : Number of formulae : 64 ( 9 unt; 49 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 8 |; 3 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 34 >; 47 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 45 ( 45 usr; 15 con; 0-5 aty)
% Number of variables : 27 ( 0 sgn; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
fun: ( $i * $i ) > $i ).
tff(decl_23,type,
combb: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
ti: ( $i * $i ) > $i ).
tff(decl_25,type,
combc: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
combi: $i > $i ).
tff(decl_27,type,
combs: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
bool: $i ).
tff(decl_29,type,
nat: $i ).
tff(decl_30,type,
finite_card: $i > $i ).
tff(decl_31,type,
finite_finite: $i > $i ).
tff(decl_32,type,
minus_minus: $i > $i ).
tff(decl_33,type,
undefined: $i > $i ).
tff(decl_34,type,
suc: $i ).
tff(decl_35,type,
preorder: $i > $o ).
tff(decl_36,type,
ord_less_eq: $i > $i ).
tff(decl_37,type,
collect: $i > $i ).
tff(decl_38,type,
image: ( $i * $i ) > $i ).
tff(decl_39,type,
insert: $i > $i ).
tff(decl_40,type,
fNot: $i ).
tff(decl_41,type,
fconj: $i ).
tff(decl_42,type,
fdisj: $i ).
tff(decl_43,type,
fequal: $i > $i ).
tff(decl_44,type,
fimplies: $i ).
tff(decl_45,type,
hAPP: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
hBOOL: $i > $o ).
tff(decl_47,type,
member: $i > $i ).
tff(decl_48,type,
x_a: $i ).
tff(decl_49,type,
g: $i ).
tff(decl_50,type,
p: $i ).
tff(decl_51,type,
pname: $i ).
tff(decl_52,type,
u: $i ).
tff(decl_53,type,
mgt_call: $i ).
tff(decl_54,type,
na: $i ).
tff(decl_55,type,
pn: $i ).
tff(decl_56,type,
finite_finite_1: $i > $o ).
tff(decl_57,type,
order: $i > $o ).
tff(decl_58,type,
esk1_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk2_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_60,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk5_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk6_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk7_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk11_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
esk12_1: $i > $i ).
tff(decl_70,type,
esk13_2: ( $i * $i ) > $i ).
fof(conj_6,conjecture,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
fof(fact_84_insert__subset,axiom,
! [X1,X14,X8,X13] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X14),X8)),X13))
<=> ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X13))
& hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X8),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__subset) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_78_imageI,axiom,
! [X2,X1,X12,X14,X8] :
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X14),X8))
=> hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X12,X14)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X12),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_imageI) ).
fof(conj_4,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
fof(c_0_5,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_6])]) ).
fof(c_0_6,plain,
! [X352,X353,X354,X355] :
( ( hBOOL(hAPP(fun(X352,bool),bool,hAPP(X352,fun(fun(X352,bool),bool),member(X352),X353),X355))
| ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),hAPP(fun(X352,bool),fun(X352,bool),hAPP(X352,fun(fun(X352,bool),fun(X352,bool)),insert(X352),X353),X354)),X355)) )
& ( hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),X354),X355))
| ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),hAPP(fun(X352,bool),fun(X352,bool),hAPP(X352,fun(fun(X352,bool),fun(X352,bool)),insert(X352),X353),X354)),X355)) )
& ( ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(X352,fun(fun(X352,bool),bool),member(X352),X353),X355))
| ~ hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),X354),X355))
| hBOOL(hAPP(fun(X352,bool),bool,hAPP(fun(X352,bool),fun(fun(X352,bool),bool),ord_less_eq(fun(X352,bool)),hAPP(fun(X352,bool),fun(X352,bool),hAPP(X352,fun(fun(X352,bool),fun(X352,bool)),insert(X352),X353),X354)),X355)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_84_insert__subset])])]) ).
cnf(c_0_7,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),hAPP(fun(x_a,bool),fun(x_a,bool),hAPP(x_a,fun(fun(x_a,bool),fun(x_a,bool)),insert(x_a),hAPP(pname,x_a,mgt_call,pn)),g)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),X4)),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,hypothesis,
hBOOL(hAPP(fun(x_a,bool),bool,hAPP(fun(x_a,bool),fun(fun(x_a,bool),bool),ord_less_eq(fun(x_a,bool)),g),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(split_conjunct,[status(thm)],[conj_1]) ).
fof(c_0_10,plain,
! [X327,X328,X329,X330,X331] :
( ~ hBOOL(hAPP(fun(X328,bool),bool,hAPP(X328,fun(fun(X328,bool),bool),member(X328),X330),X331))
| hBOOL(hAPP(fun(X327,bool),bool,hAPP(X327,fun(fun(X327,bool),bool),member(X327),hAPP(X328,X327,X329,X330)),hAPP(fun(X328,bool),fun(X327,bool),hAPP(fun(X328,X327),fun(fun(X328,bool),fun(X327,bool)),image(X328,X327),X329),X331))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_78_imageI])]) ).
cnf(c_0_11,negated_conjecture,
~ hBOOL(hAPP(fun(x_a,bool),bool,hAPP(x_a,fun(fun(x_a,bool),bool),member(x_a),hAPP(pname,x_a,mgt_call,pn)),hAPP(fun(pname,bool),fun(x_a,bool),hAPP(fun(pname,x_a),fun(fun(pname,bool),fun(x_a,bool)),image(pname,x_a),mgt_call),u))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
cnf(c_0_12,plain,
( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(fun(X1,bool),fun(X4,bool),hAPP(fun(X1,X4),fun(fun(X1,bool),fun(X4,bool)),image(X1,X4),X5),X3)))
| ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,hypothesis,
hBOOL(hAPP(fun(pname,bool),bool,hAPP(pname,fun(fun(pname,bool),bool),member(pname),pn),u)),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.39 % Computer : n018.cluster.edu
% 0.16/0.39 % Model : x86_64 x86_64
% 0.16/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39 % Memory : 8042.1875MB
% 0.16/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39 % CPULimit : 300
% 0.16/0.39 % WCLimit : 300
% 0.16/0.39 % DateTime : Sun Aug 27 20:36:16 EDT 2023
% 0.16/0.39 % CPUTime :
% 0.24/0.65 start to proof: theBenchmark
% 0.67/0.83 % Version : CSE_E---1.5
% 0.67/0.83 % Problem : theBenchmark.p
% 0.67/0.83 % Proof found
% 0.67/0.83 % SZS status Theorem for theBenchmark.p
% 0.67/0.83 % SZS output start Proof
% See solution above
% 0.67/0.84 % Total time : 0.168000 s
% 0.67/0.84 % SZS output end Proof
% 0.67/0.84 % Total time : 0.178000 s
%------------------------------------------------------------------------------