TSTP Solution File: SEU343+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU343+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 : n012.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 16:24:36 EDT 2023
% Result : Theorem 56.98s 57.06s
% Output : CNFRefutation 56.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 69
% Syntax : Number of formulae : 130 ( 14 unt; 55 typ; 0 def)
% Number of atoms : 277 ( 64 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 342 ( 140 ~; 128 |; 46 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 42 >; 36 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 13 con; 0-6 aty)
% Number of variables : 140 ( 4 sgn; 82 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
latt_str: $i > $o ).
tff(decl_23,type,
strict_latt_str: $i > $o ).
tff(decl_24,type,
the_carrier: $i > $i ).
tff(decl_25,type,
the_L_join: $i > $i ).
tff(decl_26,type,
the_L_meet: $i > $i ).
tff(decl_27,type,
latt_str_of: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
in: ( $i * $i ) > $o ).
tff(decl_29,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
relation: $i > $o ).
tff(decl_33,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_34,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_35,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_36,type,
subset_union2: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
subset_intersection2: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
function: $i > $o ).
tff(decl_39,type,
apply_binary: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_41,type,
apply: ( $i * $i ) > $i ).
tff(decl_42,type,
boole_lattice: $i > $i ).
tff(decl_43,type,
empty_carrier: $i > $o ).
tff(decl_44,type,
join_semilatt_str: $i > $o ).
tff(decl_45,type,
join: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_47,type,
meet_semilatt_str: $i > $o ).
tff(decl_48,type,
meet: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
singleton: $i > $i ).
tff(decl_50,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
empty: $i > $o ).
tff(decl_53,type,
one_sorted_str: $i > $o ).
tff(decl_54,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
empty_set: $i ).
tff(decl_56,type,
subset: ( $i * $i ) > $o ).
tff(decl_57,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk3_0: $i ).
tff(decl_60,type,
esk4_0: $i ).
tff(decl_61,type,
esk5_0: $i ).
tff(decl_62,type,
esk6_0: $i ).
tff(decl_63,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk8_1: $i > $i ).
tff(decl_65,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk10_1: $i > $i ).
tff(decl_67,type,
esk11_0: $i ).
tff(decl_68,type,
esk12_1: $i > $i ).
tff(decl_69,type,
esk13_0: $i ).
tff(decl_70,type,
esk14_0: $i ).
tff(decl_71,type,
esk15_0: $i ).
tff(decl_72,type,
esk16_1: $i > $i ).
tff(decl_73,type,
esk17_0: $i ).
tff(decl_74,type,
esk18_0: $i ).
tff(decl_75,type,
esk19_0: $i ).
tff(decl_76,type,
esk20_0: $i ).
fof(d2_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_lattices) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
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_u1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(t1_lattice3,conjecture,
! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_lattice3) ).
fof(d1_lattice3,axiom,
! [X1,X2] :
( ( strict_latt_str(X2)
& latt_str(X2) )
=> ( X2 = boole_lattice(X1)
<=> ( the_carrier(X2) = powerset(X1)
& ! [X3] :
( element(X3,powerset(X1))
=> ! [X4] :
( element(X4,powerset(X1))
=> ( apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4)
& apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(d1_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(c_0_14,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[d2_lattices]) ).
fof(c_0_15,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( ~ empty(X1)
& ~ empty(X2)
& function(X4)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& element(X5,X1)
& element(X6,X2) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_binop_1]) ).
fof(c_0_16,plain,
! [X136,X137,X138] :
( ( ~ relation_of2_as_subset(X138,X136,X137)
| relation_of2(X138,X136,X137) )
& ( ~ relation_of2(X138,X136,X137)
| relation_of2_as_subset(X138,X136,X137) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_17,plain,
! [X70] :
( ( function(the_L_meet(X70))
| ~ meet_semilatt_str(X70) )
& ( quasi_total(the_L_meet(X70),cartesian_product2(the_carrier(X70),the_carrier(X70)),the_carrier(X70))
| ~ meet_semilatt_str(X70) )
& ( relation_of2_as_subset(the_L_meet(X70),cartesian_product2(the_carrier(X70),the_carrier(X70)),the_carrier(X70))
| ~ meet_semilatt_str(X70) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t1_lattice3]) ).
fof(c_0_19,plain,
! [X28,X29,X30,X31] :
( ( the_carrier(X29) = powerset(X28)
| X29 != boole_lattice(X28)
| ~ strict_latt_str(X29)
| ~ latt_str(X29) )
& ( apply_binary(the_L_join(X29),X30,X31) = subset_union2(X28,X30,X31)
| ~ element(X31,powerset(X28))
| ~ element(X30,powerset(X28))
| X29 != boole_lattice(X28)
| ~ strict_latt_str(X29)
| ~ latt_str(X29) )
& ( apply_binary(the_L_meet(X29),X30,X31) = subset_intersection2(X28,X30,X31)
| ~ element(X31,powerset(X28))
| ~ element(X30,powerset(X28))
| X29 != boole_lattice(X28)
| ~ strict_latt_str(X29)
| ~ latt_str(X29) )
& ( element(esk1_2(X28,X29),powerset(X28))
| the_carrier(X29) != powerset(X28)
| X29 = boole_lattice(X28)
| ~ strict_latt_str(X29)
| ~ latt_str(X29) )
& ( element(esk2_2(X28,X29),powerset(X28))
| the_carrier(X29) != powerset(X28)
| X29 = boole_lattice(X28)
| ~ strict_latt_str(X29)
| ~ latt_str(X29) )
& ( apply_binary(the_L_join(X29),esk1_2(X28,X29),esk2_2(X28,X29)) != subset_union2(X28,esk1_2(X28,X29),esk2_2(X28,X29))
| apply_binary(the_L_meet(X29),esk1_2(X28,X29),esk2_2(X28,X29)) != subset_intersection2(X28,esk1_2(X28,X29),esk2_2(X28,X29))
| the_carrier(X29) != powerset(X28)
| X29 = boole_lattice(X28)
| ~ strict_latt_str(X29)
| ~ latt_str(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_lattice3])])])])]) ).
fof(c_0_20,plain,
! [X45] :
( strict_latt_str(boole_lattice(X45))
& latt_str(boole_lattice(X45)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_21,plain,
! [X37,X38,X39] :
( empty_carrier(X37)
| ~ meet_semilatt_str(X37)
| ~ element(X38,the_carrier(X37))
| ~ element(X39,the_carrier(X37))
| meet(X37,X38,X39) = apply_binary_as_element(the_carrier(X37),the_carrier(X37),the_carrier(X37),the_L_meet(X37),X38,X39) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_22,plain,
! [X124,X125,X126,X127,X128,X129] :
( empty(X124)
| empty(X125)
| ~ function(X127)
| ~ quasi_total(X127,cartesian_product2(X124,X125),X126)
| ~ relation_of2(X127,cartesian_product2(X124,X125),X126)
| ~ element(X128,X124)
| ~ element(X129,X125)
| apply_binary_as_element(X124,X125,X126,X127,X128,X129) = apply_binary(X127,X128,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_23,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,negated_conjecture,
( element(esk19_0,the_carrier(boole_lattice(esk18_0)))
& element(esk20_0,the_carrier(boole_lattice(esk18_0)))
& ( join(boole_lattice(esk18_0),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| meet(boole_lattice(esk18_0),esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_26,plain,
( the_carrier(X1) = powerset(X2)
| X1 != boole_lattice(X2)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_29,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_30,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_31,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) ) ) ),
inference(fof_simplification,[status(thm)],[d1_lattices]) ).
fof(c_0_32,plain,
! [X71] :
( ( function(the_L_join(X71))
| ~ join_semilatt_str(X71) )
& ( quasi_total(the_L_join(X71),cartesian_product2(the_carrier(X71),the_carrier(X71)),the_carrier(X71))
| ~ join_semilatt_str(X71) )
& ( relation_of2_as_subset(the_L_join(X71),cartesian_product2(the_carrier(X71),the_carrier(X71)),the_carrier(X71))
| ~ join_semilatt_str(X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
cnf(c_0_33,plain,
( empty_carrier(X1)
| meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
( empty(X1)
| empty(X2)
| apply_binary_as_element(X1,X2,X4,X3,X5,X6) = apply_binary(X3,X5,X6)
| ~ function(X3)
| ~ quasi_total(X3,cartesian_product2(X1,X2),X4)
| ~ relation_of2(X3,cartesian_product2(X1,X2),X4)
| ~ element(X5,X1)
| ~ element(X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,plain,
( relation_of2(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_38,negated_conjecture,
element(esk20_0,the_carrier(boole_lattice(esk18_0))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_39,plain,
the_carrier(boole_lattice(X1)) = powerset(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]),c_0_28])]) ).
cnf(c_0_40,negated_conjecture,
element(esk19_0,the_carrier(boole_lattice(esk18_0))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_41,plain,
! [X86] : ~ empty(powerset(X86)),
inference(variable_rename,[status(thm)],[c_0_29]) ).
fof(c_0_42,plain,
! [X84] :
( ~ empty_carrier(boole_lattice(X84))
& strict_latt_str(boole_lattice(X84)) ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
fof(c_0_43,plain,
! [X34,X35,X36] :
( empty_carrier(X34)
| ~ join_semilatt_str(X34)
| ~ element(X35,the_carrier(X34))
| ~ element(X36,the_carrier(X34))
| join(X34,X35,X36) = apply_binary_as_element(the_carrier(X34),the_carrier(X34),the_carrier(X34),the_L_join(X34),X35,X36) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_44,plain,
( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,negated_conjecture,
( join(boole_lattice(esk18_0),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| meet(boole_lattice(esk18_0),esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_46,plain,
( meet(X1,X2,X3) = apply_binary(the_L_meet(X1),X2,X3)
| empty(the_carrier(X1))
| empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_47,negated_conjecture,
element(esk20_0,powerset(esk18_0)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
element(esk19_0,powerset(esk18_0)),
inference(rw,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_49,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( empty_carrier(X1)
| join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_53,plain,
( quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_54,plain,
( relation_of2(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_44]) ).
cnf(c_0_55,negated_conjecture,
( apply_binary(the_L_meet(boole_lattice(esk18_0)),esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0)
| join(boole_lattice(esk18_0),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0)) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39]),c_0_39]),c_0_47]),c_0_39]),c_0_48])]),c_0_49]),c_0_50]) ).
cnf(c_0_56,plain,
( join(X1,X2,X3) = apply_binary(the_L_join(X1),X2,X3)
| empty(the_carrier(X1))
| empty_carrier(X1)
| ~ join_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_52]),c_0_53]),c_0_54]) ).
cnf(c_0_57,plain,
( apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X4,X2,X3)
| ~ element(X3,powerset(X4))
| ~ element(X2,powerset(X4))
| X1 != boole_lattice(X4)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_58,negated_conjecture,
( apply_binary(the_L_meet(boole_lattice(esk18_0)),esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0)
| apply_binary(the_L_join(boole_lattice(esk18_0)),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0))
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(sr,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_39]),c_0_39]),c_0_47]),c_0_39]),c_0_48])]),c_0_49]),c_0_50]) ).
cnf(c_0_59,plain,
( apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = subset_intersection2(X1,X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_57]),c_0_27]),c_0_28])]) ).
cnf(c_0_60,plain,
( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X4,X2,X3)
| ~ element(X3,powerset(X4))
| ~ element(X2,powerset(X4))
| X1 != boole_lattice(X4)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_61,negated_conjecture,
( apply_binary(the_L_join(boole_lattice(esk18_0)),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| subset_intersection2(esk18_0,esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0))
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_47]),c_0_48])]) ).
cnf(c_0_62,plain,
( apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = subset_union2(X1,X2,X3)
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_60]),c_0_27]),c_0_28])]) ).
fof(c_0_63,plain,
! [X133,X134,X135] :
( ~ element(X134,powerset(X133))
| ~ element(X135,powerset(X133))
| subset_intersection2(X133,X134,X135) = set_intersection2(X134,X135) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
cnf(c_0_64,negated_conjecture,
( subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| subset_intersection2(esk18_0,esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0))
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_47]),c_0_48])]) ).
cnf(c_0_65,plain,
( subset_intersection2(X2,X1,X3) = set_intersection2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_66,plain,
! [X130,X131,X132] :
( ~ element(X131,powerset(X130))
| ~ element(X132,powerset(X130))
| subset_union2(X130,X131,X132) = set_union2(X131,X132) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_67,negated_conjecture,
( subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0))
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_47]),c_0_48])]) ).
cnf(c_0_68,plain,
( subset_union2(X2,X1,X3) = set_union2(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_69,plain,
! [X66] :
( ( meet_semilatt_str(X66)
| ~ latt_str(X66) )
& ( join_semilatt_str(X66)
| ~ latt_str(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ meet_semilatt_str(boole_lattice(esk18_0))
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_47]),c_0_48])]) ).
cnf(c_0_71,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
~ join_semilatt_str(boole_lattice(esk18_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_28])]) ).
cnf(c_0_73,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n012.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 20:43:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 56.98/57.06 % Version : CSE_E---1.5
% 56.98/57.06 % Problem : theBenchmark.p
% 56.98/57.06 % Proof found
% 56.98/57.06 % SZS status Theorem for theBenchmark.p
% 56.98/57.06 % SZS output start Proof
% See solution above
% 56.98/57.07 % Total time : 56.462000 s
% 56.98/57.07 % SZS output end Proof
% 56.98/57.07 % Total time : 56.469000 s
%------------------------------------------------------------------------------