TSTP Solution File: SEU045+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU045+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 : n009.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 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 33
% Syntax : Number of formulae : 47 ( 5 unt; 29 typ; 0 def)
% Number of atoms : 136 ( 23 equ)
% Maximal formula atoms : 79 ( 7 avg)
% Number of connectives : 196 ( 78 ~; 86 |; 21 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 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 : 36 ( 3 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(t87_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
=> apply(relation_rng_restriction(X1,X3),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t87_funct_1) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_rng_restriction(X1,X3)))
=> apply(relation_rng_restriction(X1,X3),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t87_funct_1]) ).
fof(c_0_5,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_6,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_7,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_8,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0)))
& apply(relation_rng_restriction(esk12_0,esk14_0),esk13_0) != apply(esk14_0,esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_9,plain,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_rng_restriction(X4,X3)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
apply(relation_rng_restriction(esk12_0,esk14_0),esk13_0) != apply(esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( apply(relation_rng_restriction(X1,X2),X3) = apply(X2,X3)
| ~ in(X3,relation_dom(relation_rng_restriction(X1,X2)))
| ~ function(X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]),c_0_11]) ).
cnf(c_0_14,negated_conjecture,
in(esk13_0,relation_dom(relation_rng_restriction(esk12_0,esk14_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[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]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n009.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 : Wed Aug 23 18:28:06 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.016000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.019000 s
%------------------------------------------------------------------------------