TSTP Solution File: SEU032+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU032+1 : 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 : n014.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 16:22:12 EDT 2023
% Result : Theorem 0.17s 0.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 33
% Syntax : Number of formulae : 58 ( 11 unt; 27 typ; 0 def)
% Number of atoms : 113 ( 27 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 134 ( 52 ~; 49 |; 19 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 17 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn; 14 !; 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,
identity_relation: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
relation_empty_yielding: $i > $o ).
tff(decl_33,type,
powerset: $i > $i ).
tff(decl_34,type,
relation_dom: $i > $i ).
tff(decl_35,type,
relation_rng: $i > $i ).
tff(decl_36,type,
subset: ( $i * $i ) > $o ).
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_0: $i ).
fof(t65_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(function_inverse(X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_funct_1) ).
fof(t61_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> ( relation_composition(X1,function_inverse(X1)) = identity_relation(relation_dom(X1))
& relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_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(t62_funct_1,axiom,
! [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(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(t63_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( one_to_one(X1)
& relation_rng(X1) = relation_dom(X2)
& relation_composition(X1,X2) = identity_relation(relation_dom(X1)) )
=> X2 = function_inverse(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_funct_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
=> function_inverse(function_inverse(X1)) = X1 ) ),
inference(assume_negation,[status(cth)],[t65_funct_1]) ).
fof(c_0_7,plain,
! [X53] :
( ( relation_composition(X53,function_inverse(X53)) = identity_relation(relation_dom(X53))
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( relation_composition(function_inverse(X53),X53) = identity_relation(relation_rng(X53))
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_funct_1])])]) ).
fof(c_0_8,negated_conjecture,
( relation(esk12_0)
& function(esk12_0)
& one_to_one(esk12_0)
& function_inverse(function_inverse(esk12_0)) != esk12_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X49] :
( ( relation_rng(X49) = relation_dom(function_inverse(X49))
| ~ one_to_one(X49)
| ~ relation(X49)
| ~ function(X49) )
& ( relation_dom(X49) = relation_rng(function_inverse(X49))
| ~ one_to_one(X49)
| ~ relation(X49)
| ~ function(X49) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_funct_1])])]) ).
fof(c_0_10,plain,
! [X54] :
( ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X54)
| one_to_one(function_inverse(X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t62_funct_1])]) ).
fof(c_0_11,plain,
! [X9] :
( ( relation(function_inverse(X9))
| ~ relation(X9)
| ~ function(X9) )
& ( function(function_inverse(X9))
| ~ relation(X9)
| ~ function(X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])]) ).
fof(c_0_12,plain,
! [X55,X56] :
( ~ relation(X55)
| ~ function(X55)
| ~ relation(X56)
| ~ function(X56)
| ~ one_to_one(X55)
| relation_rng(X55) != relation_dom(X56)
| relation_composition(X55,X56) != identity_relation(relation_dom(X55))
| X56 = function_inverse(X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_funct_1])])]) ).
cnf(c_0_13,plain,
( relation_composition(function_inverse(X1),X1) = identity_relation(relation_rng(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
one_to_one(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
( relation_rng(X1) = relation_dom(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( relation_dom(X1) = relation_rng(function_inverse(X1))
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( one_to_one(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( X2 = function_inverse(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ one_to_one(X1)
| relation_rng(X1) != relation_dom(X2)
| relation_composition(X1,X2) != identity_relation(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
relation_composition(function_inverse(esk12_0),esk12_0) = identity_relation(relation_rng(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_24,negated_conjecture,
relation_dom(function_inverse(esk12_0)) = relation_rng(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_25,negated_conjecture,
relation_rng(function_inverse(esk12_0)) = relation_dom(esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_26,negated_conjecture,
one_to_one(function_inverse(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_27,negated_conjecture,
relation(function_inverse(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_15]),c_0_16])]) ).
cnf(c_0_28,negated_conjecture,
function(function_inverse(esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
function_inverse(function_inverse(esk12_0)) != esk12_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[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_25]),c_0_26]),c_0_15]),c_0_27]),c_0_16]),c_0_28])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 23 12:10:19 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.50 start to proof: theBenchmark
% 0.17/0.53 % Version : CSE_E---1.5
% 0.17/0.53 % Problem : theBenchmark.p
% 0.17/0.53 % Proof found
% 0.17/0.53 % SZS status Theorem for theBenchmark.p
% 0.17/0.53 % SZS output start Proof
% See solution above
% 0.17/0.53 % Total time : 0.019000 s
% 0.17/0.53 % SZS output end Proof
% 0.17/0.53 % Total time : 0.021000 s
%------------------------------------------------------------------------------