TSTP Solution File: SEU044+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU044+1 : 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 : n002.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 16:22:14 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 33
% Syntax : Number of formulae : 56 ( 6 unt; 29 typ; 0 def)
% Number of atoms : 177 ( 19 equ)
% Maximal formula atoms : 79 ( 6 avg)
% Number of connectives : 255 ( 105 ~; 115 |; 24 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 17 >; 9 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 50 ( 4 sgn; 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
empty_set: $i ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
relation_empty_yielding: $i > $o ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
function: $i > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
relation_dom: $i > $i ).
tff(decl_32,type,
in: ( $i * $i ) > $o ).
tff(decl_33,type,
relation_rng_restriction: ( $i * $i ) > $i ).
tff(decl_34,type,
apply: ( $i * $i ) > $i ).
tff(decl_35,type,
esk1_1: $i > $i ).
tff(decl_36,type,
esk2_0: $i ).
tff(decl_37,type,
esk3_0: $i ).
tff(decl_38,type,
esk4_0: $i ).
tff(decl_39,type,
esk5_1: $i > $i ).
tff(decl_40,type,
esk6_1: $i > $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_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
tff(decl_49,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk16_3: ( $i * $i * $i ) > $i ).
fof(t85_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_rng_restriction(X1,X3)
<=> ( ! [X4] :
( in(X4,relation_dom(X2))
<=> ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) )
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(fc5_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(t86_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_funct_1) ).
fof(c_0_4,plain,
! [X52,X53,X54,X55,X56,X57] :
( ( in(X55,relation_dom(X54))
| ~ in(X55,relation_dom(X53))
| X53 != relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( in(apply(X54,X55),X52)
| ~ in(X55,relation_dom(X53))
| X53 != relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( ~ in(X56,relation_dom(X54))
| ~ in(apply(X54,X56),X52)
| in(X56,relation_dom(X53))
| X53 != relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( ~ in(X57,relation_dom(X53))
| apply(X53,X57) = apply(X54,X57)
| X53 != relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( in(esk16_3(X52,X53,X54),relation_dom(X53))
| ~ in(esk15_3(X52,X53,X54),relation_dom(X53))
| ~ in(esk15_3(X52,X53,X54),relation_dom(X54))
| ~ in(apply(X54,esk15_3(X52,X53,X54)),X52)
| X53 = relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( apply(X53,esk16_3(X52,X53,X54)) != apply(X54,esk16_3(X52,X53,X54))
| ~ in(esk15_3(X52,X53,X54),relation_dom(X53))
| ~ in(esk15_3(X52,X53,X54),relation_dom(X54))
| ~ in(apply(X54,esk15_3(X52,X53,X54)),X52)
| X53 = relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( in(esk16_3(X52,X53,X54),relation_dom(X53))
| in(esk15_3(X52,X53,X54),relation_dom(X54))
| in(esk15_3(X52,X53,X54),relation_dom(X53))
| X53 = relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( apply(X53,esk16_3(X52,X53,X54)) != apply(X54,esk16_3(X52,X53,X54))
| in(esk15_3(X52,X53,X54),relation_dom(X54))
| in(esk15_3(X52,X53,X54),relation_dom(X53))
| X53 = relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( in(esk16_3(X52,X53,X54),relation_dom(X53))
| in(apply(X54,esk15_3(X52,X53,X54)),X52)
| in(esk15_3(X52,X53,X54),relation_dom(X53))
| X53 = relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ relation(X53)
| ~ function(X53) )
& ( apply(X53,esk16_3(X52,X53,X54)) != apply(X54,esk16_3(X52,X53,X54))
| in(apply(X54,esk15_3(X52,X53,X54)),X52)
| in(esk15_3(X52,X53,X54),relation_dom(X53))
| X53 = relation_rng_restriction(X52,X54)
| ~ relation(X54)
| ~ function(X54)
| ~ 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)],[t85_funct_1])])])])])]) ).
fof(c_0_5,plain,
! [X29,X30] :
( ~ relation(X30)
| relation(relation_rng_restriction(X29,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(c_0_6,plain,
! [X31,X32] :
( ( relation(relation_rng_restriction(X31,X32))
| ~ relation(X32)
| ~ function(X32) )
& ( function(relation_rng_restriction(X31,X32))
| ~ relation(X32)
| ~ function(X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t86_funct_1]) ).
cnf(c_0_8,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(X3))
| X3 != relation_rng_restriction(X4,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& ( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
| ~ in(esk13_0,relation_dom(esk14_0))
| ~ in(apply(esk14_0,esk13_0),esk12_0) )
& ( in(esk13_0,relation_dom(esk14_0))
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) )
& ( in(apply(esk14_0,esk13_0),esk12_0)
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_rng_restriction(X3,X2)))
| ~ function(X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_8]),c_0_9]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( in(esk13_0,relation_dom(esk14_0))
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( in(X1,relation_dom(X4))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_rng_restriction(X3,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
| ~ in(esk13_0,relation_dom(esk14_0))
| ~ in(apply(esk14_0,esk13_0),esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
in(esk13_0,relation_dom(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_19,plain,
( in(X1,relation_dom(relation_rng_restriction(X2,X3)))
| ~ in(apply(X3,X1),X2)
| ~ in(X1,relation_dom(X3))
| ~ function(X3)
| ~ relation(X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_9]),c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( in(apply(esk14_0,esk13_0),esk12_0)
| in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(X4))
| X4 != relation_rng_restriction(X3,X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X4)
| ~ function(X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
| ~ in(apply(esk14_0,esk13_0),esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]),c_0_14]),c_0_15])]) ).
cnf(c_0_24,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,relation_dom(relation_rng_restriction(X3,X1)))
| ~ function(X1)
| ~ relation(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_21]),c_0_9]),c_0_10]) ).
cnf(c_0_25,negated_conjecture,
~ in(apply(esk14_0,esk13_0),esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_14]),c_0_15])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 12:46:15 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.020000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.023000 s
%------------------------------------------------------------------------------