TSTP Solution File: SEU361+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU361+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 : 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 16:25:07 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 34
% Syntax : Number of formulae : 58 ( 10 unt; 28 typ; 0 def)
% Number of atoms : 159 ( 11 equ)
% Maximal formula atoms : 50 ( 5 avg)
% Number of connectives : 209 ( 80 ~; 76 |; 35 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 19 >; 13 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 40 ( 1 sgn; 27 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
finite: $i > $o ).
tff(decl_25,type,
rel_str: $i > $o ).
tff(decl_26,type,
bottom_of_relstr: $i > $i ).
tff(decl_27,type,
empty_set: $i ).
tff(decl_28,type,
join_on_relstr: ( $i * $i ) > $i ).
tff(decl_29,type,
the_carrier: $i > $i ).
tff(decl_30,type,
element: ( $i * $i ) > $o ).
tff(decl_31,type,
one_sorted_str: $i > $o ).
tff(decl_32,type,
empty_carrier: $i > $o ).
tff(decl_33,type,
antisymmetric_relstr: $i > $o ).
tff(decl_34,type,
ex_sup_of_relstr_set: ( $i * $i ) > $o ).
tff(decl_35,type,
relstr_set_smaller: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
related: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
lower_bounded_relstr: $i > $o ).
tff(decl_38,type,
ex_inf_of_relstr_set: ( $i * $i ) > $o ).
tff(decl_39,type,
relstr_element_smaller: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
esk1_0: $i ).
tff(decl_41,type,
esk2_0: $i ).
tff(decl_42,type,
esk3_1: $i > $i ).
tff(decl_43,type,
esk4_0: $i ).
tff(decl_44,type,
esk5_0: $i ).
tff(decl_45,type,
esk6_0: $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk9_0: $i ).
tff(decl_49,type,
esk10_0: $i ).
fof(t44_yellow_0,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_yellow_0) ).
fof(t42_yellow_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(d11_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> bottom_of_relstr(X1) = join_on_relstr(X1,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(t30_yellow_0,axiom,
! [X1] :
( ( antisymmetric_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( ( ( X2 = join_on_relstr(X1,X3)
& ex_sup_of_relstr_set(X1,X3) )
=> ( relstr_set_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X3,X4)
=> related(X1,X2,X4) ) ) ) )
& ( ( relstr_set_smaller(X1,X3,X2)
& ! [X4] :
( element(X4,the_carrier(X1))
=> ( relstr_set_smaller(X1,X3,X4)
=> related(X1,X2,X4) ) ) )
=> ( X2 = join_on_relstr(X1,X3)
& ex_sup_of_relstr_set(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_yellow_0) ).
fof(dt_k1_yellow_0,axiom,
! [X1,X2] :
( rel_str(X1)
=> element(join_on_relstr(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
fof(t6_yellow_0,axiom,
! [X1] :
( rel_str(X1)
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( relstr_set_smaller(X1,empty_set,X2)
& relstr_element_smaller(X1,empty_set,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> related(X1,bottom_of_relstr(X1),X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t44_yellow_0])]) ).
fof(c_0_7,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& antisymmetric_relstr(X1)
& lower_bounded_relstr(X1)
& rel_str(X1) )
=> ( ex_sup_of_relstr_set(X1,empty_set)
& ex_inf_of_relstr_set(X1,the_carrier(X1)) ) ),
inference(fof_simplification,[status(thm)],[t42_yellow_0]) ).
fof(c_0_8,negated_conjecture,
( ~ empty_carrier(esk9_0)
& antisymmetric_relstr(esk9_0)
& lower_bounded_relstr(esk9_0)
& rel_str(esk9_0)
& element(esk10_0,the_carrier(esk9_0))
& ~ related(esk9_0,bottom_of_relstr(esk9_0),esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X8] :
( ~ rel_str(X8)
| bottom_of_relstr(X8) = join_on_relstr(X8,empty_set) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])]) ).
fof(c_0_10,plain,
! [X26,X27,X28,X29,X30] :
( ( relstr_set_smaller(X26,X28,X27)
| X27 != join_on_relstr(X26,X28)
| ~ ex_sup_of_relstr_set(X26,X28)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( ~ element(X29,the_carrier(X26))
| ~ relstr_set_smaller(X26,X28,X29)
| related(X26,X27,X29)
| X27 != join_on_relstr(X26,X28)
| ~ ex_sup_of_relstr_set(X26,X28)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( X27 = join_on_relstr(X26,X30)
| element(esk8_3(X26,X27,X30),the_carrier(X26))
| ~ relstr_set_smaller(X26,X30,X27)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( ex_sup_of_relstr_set(X26,X30)
| element(esk8_3(X26,X27,X30),the_carrier(X26))
| ~ relstr_set_smaller(X26,X30,X27)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( X27 = join_on_relstr(X26,X30)
| relstr_set_smaller(X26,X30,esk8_3(X26,X27,X30))
| ~ relstr_set_smaller(X26,X30,X27)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( ex_sup_of_relstr_set(X26,X30)
| relstr_set_smaller(X26,X30,esk8_3(X26,X27,X30))
| ~ relstr_set_smaller(X26,X30,X27)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( X27 = join_on_relstr(X26,X30)
| ~ related(X26,X27,esk8_3(X26,X27,X30))
| ~ relstr_set_smaller(X26,X30,X27)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) )
& ( ex_sup_of_relstr_set(X26,X30)
| ~ related(X26,X27,esk8_3(X26,X27,X30))
| ~ relstr_set_smaller(X26,X30,X27)
| ~ element(X27,the_carrier(X26))
| ~ antisymmetric_relstr(X26)
| ~ rel_str(X26) ) ),
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)],[t30_yellow_0])])])])])]) ).
fof(c_0_11,plain,
! [X9,X10] :
( ~ rel_str(X9)
| element(join_on_relstr(X9,X10),the_carrier(X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_yellow_0])]) ).
fof(c_0_12,plain,
! [X32] :
( ( ex_sup_of_relstr_set(X32,empty_set)
| empty_carrier(X32)
| ~ antisymmetric_relstr(X32)
| ~ lower_bounded_relstr(X32)
| ~ rel_str(X32) )
& ( ex_inf_of_relstr_set(X32,the_carrier(X32))
| empty_carrier(X32)
| ~ antisymmetric_relstr(X32)
| ~ lower_bounded_relstr(X32)
| ~ rel_str(X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,negated_conjecture,
~ related(esk9_0,bottom_of_relstr(esk9_0),esk10_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( bottom_of_relstr(X1) = join_on_relstr(X1,empty_set)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
rel_str(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( related(X2,X4,X1)
| ~ element(X1,the_carrier(X2))
| ~ relstr_set_smaller(X2,X3,X1)
| X4 != join_on_relstr(X2,X3)
| ~ ex_sup_of_relstr_set(X2,X3)
| ~ element(X4,the_carrier(X2))
| ~ antisymmetric_relstr(X2)
| ~ rel_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( element(join_on_relstr(X1,X2),the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( ex_sup_of_relstr_set(X1,empty_set)
| empty_carrier(X1)
| ~ antisymmetric_relstr(X1)
| ~ lower_bounded_relstr(X1)
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
lower_bounded_relstr(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
antisymmetric_relstr(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
~ empty_carrier(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,negated_conjecture,
~ related(esk9_0,join_on_relstr(esk9_0,empty_set),esk10_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_23,plain,
( related(X1,join_on_relstr(X1,X2),X3)
| ~ relstr_set_smaller(X1,X2,X3)
| ~ ex_sup_of_relstr_set(X1,X2)
| ~ antisymmetric_relstr(X1)
| ~ element(X3,the_carrier(X1))
| ~ rel_str(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_16]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
ex_sup_of_relstr_set(esk9_0,empty_set),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_15])]),c_0_21]) ).
cnf(c_0_25,negated_conjecture,
element(esk10_0,the_carrier(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_26,plain,
! [X36,X37] :
( ( relstr_set_smaller(X36,empty_set,X37)
| ~ element(X37,the_carrier(X36))
| ~ rel_str(X36) )
& ( relstr_element_smaller(X36,empty_set,X37)
| ~ element(X37,the_carrier(X36))
| ~ rel_str(X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_yellow_0])])])]) ).
cnf(c_0_27,negated_conjecture,
~ relstr_set_smaller(esk9_0,empty_set,esk10_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_22,c_0_23]),c_0_24]),c_0_20]),c_0_25]),c_0_15])]) ).
cnf(c_0_28,plain,
( relstr_set_smaller(X1,empty_set,X2)
| ~ element(X2,the_carrier(X1))
| ~ rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU361+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n011.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Wed Aug 23 19:10:07 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.59 % Total time : 0.012000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.015000 s
%------------------------------------------------------------------------------