TSTP Solution File: SEU220+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU220+3 : 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 : n029.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 16:23:29 EDT 2023
% Result : Theorem 2.20s 2.34s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 37
% Syntax : Number of formulae : 60 ( 8 unt; 32 typ; 0 def)
% Number of atoms : 247 ( 72 equ)
% Maximal formula atoms : 130 ( 8 avg)
% Number of connectives : 375 ( 156 ~; 164 |; 39 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 21 >; 9 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
one_to_one: $i > $o ).
tff(decl_27,type,
function_inverse: $i > $i ).
tff(decl_28,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
empty_set: $i ).
tff(decl_31,type,
relation_empty_yielding: $i > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
relation_dom: $i > $i ).
tff(decl_34,type,
relation_rng: $i > $i ).
tff(decl_35,type,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
apply: ( $i * $i ) > $i ).
tff(decl_37,type,
esk1_1: $i > $i ).
tff(decl_38,type,
esk2_0: $i ).
tff(decl_39,type,
esk3_0: $i ).
tff(decl_40,type,
esk4_1: $i > $i ).
tff(decl_41,type,
esk5_0: $i ).
tff(decl_42,type,
esk6_0: $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_1: $i > $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk16_0: $i ).
tff(decl_53,type,
esk17_0: $i ).
fof(t57_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(t55_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_rng(X1) = relation_dom(function_inverse(X1))
& relation_dom(X1) = relation_rng(function_inverse(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t54_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = function_inverse(X1)
<=> ( relation_dom(X2) = relation_rng(X1)
& ! [X3,X4] :
( ( ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) )
=> ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) )
& ( ( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) )
=> ( in(X3,relation_rng(X1))
& X4 = apply(X2,X3) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X2)
& in(X1,relation_rng(X2)) )
=> ( X1 = apply(X2,apply(function_inverse(X2),X1))
& X1 = apply(relation_composition(function_inverse(X2),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t57_funct_1]) ).
fof(c_0_6,plain,
! [X61] :
( ( relation_rng(X61) = relation_dom(function_inverse(X61))
| ~ one_to_one(X61)
| ~ relation(X61)
| ~ function(X61) )
& ( relation_dom(X61) = relation_rng(function_inverse(X61))
| ~ one_to_one(X61)
| ~ relation(X61)
| ~ function(X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
( relation(esk17_0)
& function(esk17_0)
& one_to_one(esk17_0)
& in(esk16_0,relation_rng(esk17_0))
& ( esk16_0 != apply(esk17_0,apply(function_inverse(esk17_0),esk16_0))
| esk16_0 != apply(relation_composition(function_inverse(esk17_0),esk17_0),esk16_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X10] :
( ( relation(function_inverse(X10))
| ~ relation(X10)
| ~ function(X10) )
& ( function(function_inverse(X10))
| ~ relation(X10)
| ~ function(X10) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_9,plain,
! [X41,X42,X43] :
( ~ relation(X42)
| ~ function(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ in(X41,relation_dom(X42))
| apply(relation_composition(X42,X43),X41) = apply(X43,apply(X42,X41)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_10,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
one_to_one(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
relation_dom(function_inverse(esk17_0)) = relation_rng(esk17_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
function(function_inverse(esk17_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_13])]) ).
cnf(c_0_18,negated_conjecture,
( apply(relation_composition(function_inverse(esk17_0),X1),X2) = apply(X1,apply(function_inverse(esk17_0),X2))
| ~ relation(function_inverse(esk17_0))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_19,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,plain,
! [X51,X52,X53,X54,X55,X56] :
( ( relation_dom(X52) = relation_rng(X51)
| X52 != function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( in(X54,relation_dom(X51))
| ~ in(X53,relation_rng(X51))
| X54 != apply(X52,X53)
| X52 != function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( X53 = apply(X51,X54)
| ~ in(X53,relation_rng(X51))
| X54 != apply(X52,X53)
| X52 != function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( in(X55,relation_rng(X51))
| ~ in(X56,relation_dom(X51))
| X55 != apply(X51,X56)
| X52 != function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( X56 = apply(X52,X55)
| ~ in(X56,relation_dom(X51))
| X55 != apply(X51,X56)
| X52 != function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( in(esk15_2(X51,X52),relation_dom(X51))
| in(esk12_2(X51,X52),relation_rng(X51))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( esk14_2(X51,X52) = apply(X51,esk15_2(X51,X52))
| in(esk12_2(X51,X52),relation_rng(X51))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( ~ in(esk14_2(X51,X52),relation_rng(X51))
| esk15_2(X51,X52) != apply(X52,esk14_2(X51,X52))
| in(esk12_2(X51,X52),relation_rng(X51))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( in(esk15_2(X51,X52),relation_dom(X51))
| esk13_2(X51,X52) = apply(X52,esk12_2(X51,X52))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( esk14_2(X51,X52) = apply(X51,esk15_2(X51,X52))
| esk13_2(X51,X52) = apply(X52,esk12_2(X51,X52))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( ~ in(esk14_2(X51,X52),relation_rng(X51))
| esk15_2(X51,X52) != apply(X52,esk14_2(X51,X52))
| esk13_2(X51,X52) = apply(X52,esk12_2(X51,X52))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( in(esk15_2(X51,X52),relation_dom(X51))
| ~ in(esk13_2(X51,X52),relation_dom(X51))
| esk12_2(X51,X52) != apply(X51,esk13_2(X51,X52))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( esk14_2(X51,X52) = apply(X51,esk15_2(X51,X52))
| ~ in(esk13_2(X51,X52),relation_dom(X51))
| esk12_2(X51,X52) != apply(X51,esk13_2(X51,X52))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) )
& ( ~ in(esk14_2(X51,X52),relation_rng(X51))
| esk15_2(X51,X52) != apply(X52,esk14_2(X51,X52))
| ~ in(esk13_2(X51,X52),relation_dom(X51))
| esk12_2(X51,X52) != apply(X51,esk13_2(X51,X52))
| relation_dom(X52) != relation_rng(X51)
| X52 = function_inverse(X51)
| ~ relation(X52)
| ~ function(X52)
| ~ one_to_one(X51)
| ~ relation(X51)
| ~ function(X51) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[t54_funct_1])])])])])]) ).
cnf(c_0_21,negated_conjecture,
( esk16_0 != apply(esk17_0,apply(function_inverse(esk17_0),esk16_0))
| esk16_0 != apply(relation_composition(function_inverse(esk17_0),esk17_0),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
( apply(relation_composition(function_inverse(esk17_0),X1),X2) = apply(X1,apply(function_inverse(esk17_0),X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11]),c_0_13])]) ).
cnf(c_0_23,negated_conjecture,
in(esk16_0,relation_rng(esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,plain,
( X1 = apply(X2,X3)
| ~ in(X1,relation_rng(X2))
| X3 != apply(X4,X1)
| X4 != function_inverse(X2)
| ~ relation(X4)
| ~ function(X4)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
apply(esk17_0,apply(function_inverse(esk17_0),esk16_0)) != esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_11]),c_0_13]),c_0_23])]) ).
cnf(c_0_26,plain,
( apply(X1,apply(function_inverse(X1),X2)) = X2
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]),c_0_14]),c_0_19]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_12]),c_0_11]),c_0_13]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU220+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 14:25:37 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 2.20/2.34 % Version : CSE_E---1.5
% 2.20/2.34 % Problem : theBenchmark.p
% 2.20/2.34 % Proof found
% 2.20/2.34 % SZS status Theorem for theBenchmark.p
% 2.20/2.34 % SZS output start Proof
% See solution above
% 2.20/2.34 % Total time : 1.766000 s
% 2.20/2.34 % SZS output end Proof
% 2.20/2.34 % Total time : 1.769000 s
%------------------------------------------------------------------------------