TSTP Solution File: SEU221+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 0.55s 0.64s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 34
% Syntax : Number of formulae : 66 ( 13 unt; 29 typ; 0 def)
% Number of atoms : 278 ( 68 equ)
% Maximal formula atoms : 130 ( 7 avg)
% Number of connectives : 410 ( 169 ~; 185 |; 40 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 19 >; 8 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-2 aty)
% Number of variables : 38 ( 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,
relation_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
function_inverse: $i > $i ).
tff(decl_30,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
relation_empty_yielding: $i > $o ).
tff(decl_34,type,
relation_rng: $i > $i ).
tff(decl_35,type,
esk1_1: $i > $i ).
tff(decl_36,type,
esk2_1: $i > $i ).
tff(decl_37,type,
esk3_1: $i > $i ).
tff(decl_38,type,
esk4_0: $i ).
tff(decl_39,type,
esk5_0: $i ).
tff(decl_40,type,
esk6_0: $i ).
tff(decl_41,type,
esk7_0: $i ).
tff(decl_42,type,
esk8_0: $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk16_0: $i ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_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(t62_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_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(t57_funct_1,axiom,
! [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(c_0_5,plain,
! [X10,X11,X12] :
( ( ~ one_to_one(X10)
| ~ in(X11,relation_dom(X10))
| ~ in(X12,relation_dom(X10))
| apply(X10,X11) != apply(X10,X12)
| X11 = X12
| ~ relation(X10)
| ~ function(X10) )
& ( in(esk1_1(X10),relation_dom(X10))
| one_to_one(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( in(esk2_1(X10),relation_dom(X10))
| one_to_one(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( apply(X10,esk1_1(X10)) = apply(X10,esk2_1(X10))
| one_to_one(X10)
| ~ relation(X10)
| ~ function(X10) )
& ( esk1_1(X10) != esk2_1(X10)
| one_to_one(X10)
| ~ relation(X10)
| ~ function(X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
fof(c_0_6,plain,
! [X15] :
( ( relation(function_inverse(X15))
| ~ relation(X15)
| ~ function(X15) )
& ( function(function_inverse(X15))
| ~ relation(X15)
| ~ function(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> one_to_one(function_inverse(X1)) ) ),
inference(assume_negation,[status(cth)],[t62_funct_1]) ).
cnf(c_0_8,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( relation(esk16_0)
& function(esk16_0)
& one_to_one(esk16_0)
& ~ one_to_one(function_inverse(esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_12,plain,
! [X42,X43,X44,X45,X46,X47] :
( ( relation_dom(X43) = relation_rng(X42)
| X43 != function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( in(X45,relation_dom(X42))
| ~ in(X44,relation_rng(X42))
| X45 != apply(X43,X44)
| X43 != function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( X44 = apply(X42,X45)
| ~ in(X44,relation_rng(X42))
| X45 != apply(X43,X44)
| X43 != function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( in(X46,relation_rng(X42))
| ~ in(X47,relation_dom(X42))
| X46 != apply(X42,X47)
| X43 != function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( X47 = apply(X43,X46)
| ~ in(X47,relation_dom(X42))
| X46 != apply(X42,X47)
| X43 != function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( in(esk15_2(X42,X43),relation_dom(X42))
| in(esk12_2(X42,X43),relation_rng(X42))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( esk14_2(X42,X43) = apply(X42,esk15_2(X42,X43))
| in(esk12_2(X42,X43),relation_rng(X42))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( ~ in(esk14_2(X42,X43),relation_rng(X42))
| esk15_2(X42,X43) != apply(X43,esk14_2(X42,X43))
| in(esk12_2(X42,X43),relation_rng(X42))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( in(esk15_2(X42,X43),relation_dom(X42))
| esk13_2(X42,X43) = apply(X43,esk12_2(X42,X43))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( esk14_2(X42,X43) = apply(X42,esk15_2(X42,X43))
| esk13_2(X42,X43) = apply(X43,esk12_2(X42,X43))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( ~ in(esk14_2(X42,X43),relation_rng(X42))
| esk15_2(X42,X43) != apply(X43,esk14_2(X42,X43))
| esk13_2(X42,X43) = apply(X43,esk12_2(X42,X43))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( in(esk15_2(X42,X43),relation_dom(X42))
| ~ in(esk13_2(X42,X43),relation_dom(X42))
| esk12_2(X42,X43) != apply(X42,esk13_2(X42,X43))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( esk14_2(X42,X43) = apply(X42,esk15_2(X42,X43))
| ~ in(esk13_2(X42,X43),relation_dom(X42))
| esk12_2(X42,X43) != apply(X42,esk13_2(X42,X43))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) )
& ( ~ in(esk14_2(X42,X43),relation_rng(X42))
| esk15_2(X42,X43) != apply(X43,esk14_2(X42,X43))
| ~ in(esk13_2(X42,X43),relation_dom(X42))
| esk12_2(X42,X43) != apply(X42,esk13_2(X42,X43))
| relation_dom(X43) != relation_rng(X42)
| X43 = function_inverse(X42)
| ~ relation(X43)
| ~ function(X43)
| ~ one_to_one(X42)
| ~ relation(X42)
| ~ function(X42) ) ),
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_13,plain,
( apply(X1,esk1_1(X1)) = apply(X1,esk2_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( one_to_one(function_inverse(X1))
| in(esk2_1(function_inverse(X1)),relation_dom(function_inverse(X1)))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
~ one_to_one(function_inverse(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( relation_dom(X1) = relation_rng(X2)
| X1 != function_inverse(X2)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_20,plain,
! [X52,X53] :
( ( X52 = apply(X53,apply(function_inverse(X53),X52))
| ~ one_to_one(X53)
| ~ in(X52,relation_rng(X53))
| ~ relation(X53)
| ~ function(X53) )
& ( X52 = apply(relation_composition(function_inverse(X53),X53),X52)
| ~ one_to_one(X53)
| ~ in(X52,relation_rng(X53))
| ~ relation(X53)
| ~ function(X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
cnf(c_0_21,plain,
( apply(function_inverse(X1),esk2_1(function_inverse(X1))) = apply(function_inverse(X1),esk1_1(function_inverse(X1)))
| one_to_one(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_9]),c_0_10]) ).
cnf(c_0_22,negated_conjecture,
in(esk2_1(function_inverse(esk16_0)),relation_dom(function_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_23,plain,
( relation_dom(function_inverse(X1)) = relation_rng(X1)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_10]),c_0_9]) ).
cnf(c_0_24,negated_conjecture,
one_to_one(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_25,plain,
( one_to_one(function_inverse(X1))
| in(esk1_1(function_inverse(X1)),relation_dom(function_inverse(X1)))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_9]),c_0_10]) ).
cnf(c_0_26,plain,
( X1 = apply(X2,apply(function_inverse(X2),X1))
| ~ one_to_one(X2)
| ~ in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
apply(function_inverse(esk16_0),esk2_1(function_inverse(esk16_0))) = apply(function_inverse(esk16_0),esk1_1(function_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_28,negated_conjecture,
in(esk2_1(function_inverse(esk16_0)),relation_rng(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_15]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
in(esk1_1(function_inverse(esk16_0)),relation_dom(function_inverse(esk16_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_30,negated_conjecture,
apply(esk16_0,apply(function_inverse(esk16_0),esk1_1(function_inverse(esk16_0)))) = esk2_1(function_inverse(esk16_0)),
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_26,c_0_27]),c_0_24]),c_0_15]),c_0_16]),c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
in(esk1_1(function_inverse(esk16_0)),relation_rng(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_24]),c_0_15]),c_0_16])]) ).
cnf(c_0_32,plain,
( one_to_one(X1)
| esk1_1(X1) != esk2_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_33,negated_conjecture,
esk2_1(function_inverse(esk16_0)) = esk1_1(function_inverse(esk16_0)),
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_26,c_0_30]),c_0_24]),c_0_15]),c_0_16]),c_0_31])]) ).
cnf(c_0_34,negated_conjecture,
( ~ relation(function_inverse(esk16_0))
| ~ function(function_inverse(esk16_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17]) ).
cnf(c_0_35,negated_conjecture,
~ relation(function_inverse(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_10]),c_0_15]),c_0_16])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_9]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:20:43 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.55/0.64 % Version : CSE_E---1.5
% 0.55/0.64 % Problem : theBenchmark.p
% 0.55/0.64 % Proof found
% 0.55/0.64 % SZS status Theorem for theBenchmark.p
% 0.55/0.64 % SZS output start Proof
% See solution above
% 0.55/0.64 % Total time : 0.041000 s
% 0.55/0.64 % SZS output end Proof
% 0.55/0.64 % Total time : 0.044000 s
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