TSTP Solution File: SEU221+3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU221+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 0.20s 0.73s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 68 ( 11 unt; 33 typ; 0 def)
% Number of atoms : 278 ( 70 equ)
% Maximal formula atoms : 130 ( 7 avg)
% Number of connectives : 413 ( 170 ~; 187 |; 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 : 32 ( 23 >; 9 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-2 aty)
% Number of variables : 39 ( 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,
powerset: $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_1: $i > $i ).
tff(decl_39,type,
esk3_1: $i > $i ).
tff(decl_40,type,
esk4_0: $i ).
tff(decl_41,type,
esk5_0: $i ).
tff(decl_42,type,
esk6_1: $i > $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_0: $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_1: $i > $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk18_0: $i ).
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/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(dt_k2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( relation(function_inverse(X1))
& function(function_inverse(X1)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
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/sandbox/benchmark/theBenchmark.p',d8_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/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(c_0_5,plain,
! [X53,X54,X55,X56,X57,X58] :
( ( relation_dom(X54) = relation_rng(X53)
| X54 != function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( in(X56,relation_dom(X53))
| ~ in(X55,relation_rng(X53))
| X56 != apply(X54,X55)
| X54 != function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( X55 = apply(X53,X56)
| ~ in(X55,relation_rng(X53))
| X56 != apply(X54,X55)
| X54 != function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( in(X57,relation_rng(X53))
| ~ in(X58,relation_dom(X53))
| X57 != apply(X53,X58)
| X54 != function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( X58 = apply(X54,X57)
| ~ in(X58,relation_dom(X53))
| X57 != apply(X53,X58)
| X54 != function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( in(esk17_2(X53,X54),relation_dom(X53))
| in(esk14_2(X53,X54),relation_rng(X53))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( esk16_2(X53,X54) = apply(X53,esk17_2(X53,X54))
| in(esk14_2(X53,X54),relation_rng(X53))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( ~ in(esk16_2(X53,X54),relation_rng(X53))
| esk17_2(X53,X54) != apply(X54,esk16_2(X53,X54))
| in(esk14_2(X53,X54),relation_rng(X53))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( in(esk17_2(X53,X54),relation_dom(X53))
| esk15_2(X53,X54) = apply(X54,esk14_2(X53,X54))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( esk16_2(X53,X54) = apply(X53,esk17_2(X53,X54))
| esk15_2(X53,X54) = apply(X54,esk14_2(X53,X54))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( ~ in(esk16_2(X53,X54),relation_rng(X53))
| esk17_2(X53,X54) != apply(X54,esk16_2(X53,X54))
| esk15_2(X53,X54) = apply(X54,esk14_2(X53,X54))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( in(esk17_2(X53,X54),relation_dom(X53))
| ~ in(esk15_2(X53,X54),relation_dom(X53))
| esk14_2(X53,X54) != apply(X53,esk15_2(X53,X54))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( esk16_2(X53,X54) = apply(X53,esk17_2(X53,X54))
| ~ in(esk15_2(X53,X54),relation_dom(X53))
| esk14_2(X53,X54) != apply(X53,esk15_2(X53,X54))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) )
& ( ~ in(esk16_2(X53,X54),relation_rng(X53))
| esk17_2(X53,X54) != apply(X54,esk16_2(X53,X54))
| ~ in(esk15_2(X53,X54),relation_dom(X53))
| esk14_2(X53,X54) != apply(X53,esk15_2(X53,X54))
| relation_dom(X54) != relation_rng(X53)
| X54 = function_inverse(X53)
| ~ relation(X54)
| ~ function(X54)
| ~ one_to_one(X53)
| ~ relation(X53)
| ~ function(X53) ) ),
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])])])])])]) ).
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]) ).
fof(c_0_8,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])])])])]) ).
cnf(c_0_9,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_5]) ).
cnf(c_0_10,plain,
( function(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( relation(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,negated_conjecture,
( relation(esk18_0)
& function(esk18_0)
& one_to_one(esk18_0)
& ~ one_to_one(function_inverse(esk18_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
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_8]) ).
cnf(c_0_14,plain,
( in(esk2_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,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_9]),c_0_10]),c_0_11]) ).
cnf(c_0_16,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
one_to_one(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X63,X64] :
( ( X63 = apply(X64,apply(function_inverse(X64),X63))
| ~ one_to_one(X64)
| ~ in(X63,relation_rng(X64))
| ~ relation(X64)
| ~ function(X64) )
& ( X63 = apply(relation_composition(function_inverse(X64),X64),X63)
| ~ one_to_one(X64)
| ~ in(X63,relation_rng(X64))
| ~ relation(X64)
| ~ function(X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_funct_1])])]) ).
cnf(c_0_20,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_11]),c_0_10]) ).
cnf(c_0_21,negated_conjecture,
~ one_to_one(function_inverse(esk18_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,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_14,c_0_11]),c_0_10]) ).
cnf(c_0_23,negated_conjecture,
relation_dom(function_inverse(esk18_0)) = relation_rng(esk18_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,plain,
( in(esk1_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,plain,
( one_to_one(X1)
| esk1_1(X1) != esk2_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
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_19]) ).
cnf(c_0_27,negated_conjecture,
apply(function_inverse(esk18_0),esk2_1(function_inverse(esk18_0))) = apply(function_inverse(esk18_0),esk1_1(function_inverse(esk18_0))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_18])]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
in(esk2_1(function_inverse(esk18_0)),relation_rng(esk18_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23]),c_0_18])]),c_0_21]) ).
cnf(c_0_29,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_24,c_0_11]),c_0_10]) ).
cnf(c_0_30,plain,
( one_to_one(function_inverse(X1))
| esk2_1(function_inverse(X1)) != esk1_1(function_inverse(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_11]),c_0_10]) ).
cnf(c_0_31,negated_conjecture,
apply(esk18_0,apply(function_inverse(esk18_0),esk1_1(function_inverse(esk18_0)))) = esk2_1(function_inverse(esk18_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_17]),c_0_16]),c_0_18]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
in(esk1_1(function_inverse(esk18_0)),relation_rng(esk18_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_23]),c_0_18])]),c_0_21]) ).
cnf(c_0_33,negated_conjecture,
esk2_1(function_inverse(esk18_0)) != esk1_1(function_inverse(esk18_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_16]),c_0_18])]),c_0_21]) ).
cnf(c_0_34,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(spm,[status(thm)],[c_0_26,c_0_31]),c_0_17]),c_0_16]),c_0_18]),c_0_32])]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU221+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 00:54:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.73 % Version : CSE_E---1.5
% 0.20/0.73 % Problem : theBenchmark.p
% 0.20/0.73 % Proof found
% 0.20/0.73 % SZS status Theorem for theBenchmark.p
% 0.20/0.73 % SZS output start Proof
% See solution above
% 0.20/0.74 % Total time : 0.155000 s
% 0.20/0.74 % SZS output end Proof
% 0.20/0.74 % Total time : 0.159000 s
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