TSTP Solution File: SEU382+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 16:25:18 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 72
% Syntax : Number of formulae : 97 ( 19 unt; 64 typ; 0 def)
% Number of atoms : 65 ( 26 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 50 ( 18 ~; 14 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 49 >; 13 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 15 con; 0-2 aty)
% Number of variables : 46 ( 4 sgn; 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
rel_str: $i > $o ).
tff(decl_23,type,
strict_rel_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_InternalRel: $i > $i ).
tff(decl_26,type,
rel_str_of: ( $i * $i ) > $i ).
tff(decl_27,type,
in: ( $i * $i ) > $o ).
tff(decl_28,type,
empty_carrier: $i > $o ).
tff(decl_29,type,
reflexive_relstr: $i > $o ).
tff(decl_30,type,
complete_relstr: $i > $o ).
tff(decl_31,type,
up_complete_relstr: $i > $o ).
tff(decl_32,type,
join_complete_relstr: $i > $o ).
tff(decl_33,type,
boolean_relstr: $i > $o ).
tff(decl_34,type,
transitive_relstr: $i > $o ).
tff(decl_35,type,
antisymmetric_relstr: $i > $o ).
tff(decl_36,type,
with_suprema_relstr: $i > $o ).
tff(decl_37,type,
with_infima_relstr: $i > $o ).
tff(decl_38,type,
upper_bounded_relstr: $i > $o ).
tff(decl_39,type,
distributive_relstr: $i > $o ).
tff(decl_40,type,
heyting_relstr: $i > $o ).
tff(decl_41,type,
lower_bounded_relstr: $i > $o ).
tff(decl_42,type,
bounded_relstr: $i > $o ).
tff(decl_43,type,
empty: $i > $o ).
tff(decl_44,type,
finite: $i > $o ).
tff(decl_45,type,
v1_yellow_3: $i > $o ).
tff(decl_46,type,
powerset: $i > $i ).
tff(decl_47,type,
element: ( $i * $i ) > $o ).
tff(decl_48,type,
complemented_relstr: $i > $o ).
tff(decl_49,type,
incl_POSet: $i > $i ).
tff(decl_50,type,
inclusion_order: $i > $i ).
tff(decl_51,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
inclusion_relation: $i > $i ).
tff(decl_53,type,
relation: $i > $o ).
tff(decl_54,type,
reflexive: $i > $o ).
tff(decl_55,type,
antisymmetric: $i > $o ).
tff(decl_56,type,
transitive: $i > $o ).
tff(decl_57,type,
v1_partfun1: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_59,type,
boole_POSet: $i > $i ).
tff(decl_60,type,
one_sorted_str: $i > $o ).
tff(decl_61,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_62,type,
empty_set: $i ).
tff(decl_63,type,
subset: ( $i * $i ) > $o ).
tff(decl_64,type,
esk1_0: $i ).
tff(decl_65,type,
esk2_0: $i ).
tff(decl_66,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk4_1: $i > $i ).
tff(decl_68,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk6_0: $i ).
tff(decl_70,type,
esk7_0: $i ).
tff(decl_71,type,
esk8_0: $i ).
tff(decl_72,type,
esk9_1: $i > $i ).
tff(decl_73,type,
esk10_0: $i ).
tff(decl_74,type,
esk11_0: $i ).
tff(decl_75,type,
esk12_0: $i ).
tff(decl_76,type,
esk13_1: $i > $i ).
tff(decl_77,type,
esk14_0: $i ).
tff(decl_78,type,
esk15_0: $i ).
tff(decl_79,type,
esk16_1: $i > $i ).
tff(decl_80,type,
esk17_0: $i ).
tff(decl_81,type,
esk18_1: $i > $i ).
tff(decl_82,type,
esk19_0: $i ).
tff(decl_83,type,
esk20_1: $i > $i ).
tff(decl_84,type,
esk21_0: $i ).
tff(decl_85,type,
esk22_0: $i ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_k1_yellow_1,axiom,
! [X1] :
( reflexive(inclusion_order(X1))
& antisymmetric(inclusion_order(X1))
& transitive(inclusion_order(X1))
& v1_partfun1(inclusion_order(X1),X1,X1)
& relation_of2_as_subset(inclusion_order(X1),X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(t4_waybel_7,conjecture,
! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_waybel_7) ).
fof(free_g1_orders_2,axiom,
! [X1,X2] :
( relation_of2(X2,X1,X1)
=> ! [X3,X4] :
( rel_str_of(X1,X2) = rel_str_of(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(dt_k2_yellow_1,axiom,
! [X1] :
( strict_rel_str(incl_POSet(X1))
& rel_str(incl_POSet(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(d1_yellow_1,axiom,
! [X1] : incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(t4_yellow_1,axiom,
! [X1] : boole_POSet(X1) = incl_POSet(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_yellow_1) ).
fof(abstractness_v1_orders_2,axiom,
! [X1] :
( rel_str(X1)
=> ( strict_rel_str(X1)
=> X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(c_0_8,plain,
! [X94,X95,X96] :
( ( ~ relation_of2_as_subset(X96,X94,X95)
| relation_of2(X96,X94,X95) )
& ( ~ relation_of2(X96,X94,X95)
| relation_of2_as_subset(X96,X94,X95) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_9,plain,
! [X37] :
( reflexive(inclusion_order(X37))
& antisymmetric(inclusion_order(X37))
& transitive(inclusion_order(X37))
& v1_partfun1(inclusion_order(X37),X37,X37)
& relation_of2_as_subset(inclusion_order(X37),X37,X37) ),
inference(variable_rename,[status(thm)],[dt_k1_yellow_1]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] : the_carrier(boole_POSet(X1)) = powerset(X1),
inference(assume_negation,[status(cth)],[t4_waybel_7]) ).
fof(c_0_11,plain,
! [X68,X69,X70,X71] :
( ( X68 = X70
| rel_str_of(X68,X69) != rel_str_of(X70,X71)
| ~ relation_of2(X69,X68,X68) )
& ( X69 = X71
| rel_str_of(X68,X69) != rel_str_of(X70,X71)
| ~ relation_of2(X69,X68,X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[free_g1_orders_2])])])]) ).
cnf(c_0_12,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
relation_of2_as_subset(inclusion_order(X1),X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X38] :
( strict_rel_str(incl_POSet(X38))
& rel_str(incl_POSet(X38)) ),
inference(variable_rename,[status(thm)],[dt_k2_yellow_1]) ).
fof(c_0_15,plain,
! [X33] : incl_POSet(X33) = rel_str_of(X33,inclusion_order(X33)),
inference(variable_rename,[status(thm)],[d1_yellow_1]) ).
fof(c_0_16,negated_conjecture,
the_carrier(boole_POSet(esk22_0)) != powerset(esk22_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_17,plain,
! [X108] : boole_POSet(X108) = incl_POSet(powerset(X108)),
inference(variable_rename,[status(thm)],[t4_yellow_1]) ).
cnf(c_0_18,plain,
( X1 = X2
| rel_str_of(X1,X3) != rel_str_of(X2,X4)
| ~ relation_of2(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
relation_of2(inclusion_order(X1),X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_20,plain,
! [X5] :
( ~ rel_str(X5)
| ~ strict_rel_str(X5)
| X5 = rel_str_of(the_carrier(X5),the_InternalRel(X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[abstractness_v1_orders_2])]) ).
cnf(c_0_21,plain,
strict_rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
incl_POSet(X1) = rel_str_of(X1,inclusion_order(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
rel_str(incl_POSet(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,negated_conjecture,
the_carrier(boole_POSet(esk22_0)) != powerset(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
boole_POSet(X1) = incl_POSet(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( X1 = X2
| rel_str_of(X1,inclusion_order(X1)) != rel_str_of(X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( X1 = rel_str_of(the_carrier(X1),the_InternalRel(X1))
| ~ rel_str(X1)
| ~ strict_rel_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
strict_rel_str(rel_str_of(X1,inclusion_order(X1))),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
rel_str(rel_str_of(X1,inclusion_order(X1))),
inference(rw,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_30,negated_conjecture,
the_carrier(rel_str_of(powerset(esk22_0),inclusion_order(powerset(esk22_0)))) != powerset(esk22_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_22]) ).
cnf(c_0_31,plain,
the_carrier(rel_str_of(X1,inclusion_order(X1))) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])]),c_0_28]),c_0_29])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 12:57:35 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.029000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.034000 s
%------------------------------------------------------------------------------