TSTP Solution File: SEU342+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU342+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 : n017.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 70.93s 71.02s
% Output : CNFRefutation 71.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 56
% Syntax : Number of formulae : 172 ( 26 unt; 41 typ; 0 def)
% Number of atoms : 454 ( 75 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 498 ( 175 ~; 222 |; 72 &)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 30 >; 15 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-4 aty)
% Number of variables : 187 ( 16 sgn; 74 !; 5 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
latt_str: $i > $o ).
tff(decl_24,type,
empty_carrier: $i > $o ).
tff(decl_25,type,
lattice: $i > $o ).
tff(decl_26,type,
join_commutative: $i > $o ).
tff(decl_27,type,
join_associative: $i > $o ).
tff(decl_28,type,
meet_commutative: $i > $o ).
tff(decl_29,type,
meet_associative: $i > $o ).
tff(decl_30,type,
meet_absorbing: $i > $o ).
tff(decl_31,type,
join_absorbing: $i > $o ).
tff(decl_32,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_33,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_34,type,
singleton: $i > $i ).
tff(decl_35,type,
relation_of_lattice: $i > $i ).
tff(decl_36,type,
a_1_0_filter_1: $i > $i ).
tff(decl_37,type,
empty: $i > $o ).
tff(decl_38,type,
element: ( $i * $i ) > $o ).
tff(decl_39,type,
ordered_pair_as_product_element: ( $i * $i * $i * $i ) > $i ).
tff(decl_40,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_41,type,
relation: $i > $o ).
tff(decl_42,type,
meet_semilatt_str: $i > $o ).
tff(decl_43,type,
one_sorted_str: $i > $o ).
tff(decl_44,type,
join_semilatt_str: $i > $o ).
tff(decl_45,type,
the_carrier: $i > $i ).
tff(decl_46,type,
empty_set: $i ).
tff(decl_47,type,
below_refl: ( $i * $i * $i ) > $o ).
tff(decl_48,type,
below: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
esk1_0: $i ).
tff(decl_50,type,
esk2_0: $i ).
tff(decl_51,type,
esk3_0: $i ).
tff(decl_52,type,
esk4_0: $i ).
tff(decl_53,type,
esk5_1: $i > $i ).
tff(decl_54,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk8_0: $i ).
tff(decl_57,type,
esk9_0: $i ).
tff(decl_58,type,
esk10_0: $i ).
tff(decl_59,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk12_0: $i ).
tff(decl_61,type,
esk13_0: $i ).
tff(decl_62,type,
esk14_0: $i ).
fof(fraenkel_a_1_0_filter_1,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_1_0_filter_1) ).
fof(t32_filter_1,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
fof(cc1_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(reflexivity_r3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> below_refl(X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r3_lattices) ).
fof(d8_filter_1,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_filter_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(redefinition_k1_domain_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t33_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(dt_l1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(c_0_15,plain,
! [X1,X2] :
( ( ~ empty_carrier(X2)
& lattice(X2)
& latt_str(X2) )
=> ( in(X1,a_1_0_filter_1(X2))
<=> ? [X3,X4] :
( element(X3,the_carrier(X2))
& element(X4,the_carrier(X2))
& X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X3,X4)
& below_refl(X2,X3,X4) ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_1_0_filter_1]) ).
fof(c_0_16,plain,
! [X34,X35,X38,X39] :
( ( element(esk6_2(X34,X35),the_carrier(X35))
| ~ in(X34,a_1_0_filter_1(X35))
| empty_carrier(X35)
| ~ lattice(X35)
| ~ latt_str(X35) )
& ( element(esk7_2(X34,X35),the_carrier(X35))
| ~ in(X34,a_1_0_filter_1(X35))
| empty_carrier(X35)
| ~ lattice(X35)
| ~ latt_str(X35) )
& ( X34 = ordered_pair_as_product_element(the_carrier(X35),the_carrier(X35),esk6_2(X34,X35),esk7_2(X34,X35))
| ~ in(X34,a_1_0_filter_1(X35))
| empty_carrier(X35)
| ~ lattice(X35)
| ~ latt_str(X35) )
& ( below_refl(X35,esk6_2(X34,X35),esk7_2(X34,X35))
| ~ in(X34,a_1_0_filter_1(X35))
| empty_carrier(X35)
| ~ lattice(X35)
| ~ latt_str(X35) )
& ( ~ element(X38,the_carrier(X35))
| ~ element(X39,the_carrier(X35))
| X34 != ordered_pair_as_product_element(the_carrier(X35),the_carrier(X35),X38,X39)
| ~ below_refl(X35,X38,X39)
| in(X34,a_1_0_filter_1(X35))
| empty_carrier(X35)
| ~ lattice(X35)
| ~ latt_str(X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),relation_of_lattice(X1))
<=> below_refl(X1,X2,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t32_filter_1])]) ).
cnf(c_0_18,plain,
( in(X4,a_1_0_filter_1(X2))
| empty_carrier(X2)
| ~ element(X1,the_carrier(X2))
| ~ element(X3,the_carrier(X2))
| X4 != ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),X1,X3)
| ~ below_refl(X2,X1,X3)
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,negated_conjecture,
( ~ empty_carrier(esk12_0)
& lattice(esk12_0)
& latt_str(esk12_0)
& element(esk13_0,the_carrier(esk12_0))
& element(esk14_0,the_carrier(esk12_0))
& ( ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| ~ below_refl(esk12_0,esk13_0,esk14_0) )
& ( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_20,plain,
! [X1] :
( latt_str(X1)
=> ( ( ~ empty_carrier(X1)
& lattice(X1) )
=> ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_associative(X1)
& meet_commutative(X1)
& meet_associative(X1)
& meet_absorbing(X1)
& join_absorbing(X1) ) ) ),
inference(fof_simplification,[status(thm)],[cc1_lattices]) ).
cnf(c_0_21,plain,
( empty_carrier(X1)
| in(ordered_pair_as_product_element(the_carrier(X1),the_carrier(X1),X2,X3),a_1_0_filter_1(X1))
| ~ below_refl(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
element(esk13_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
lattice(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
latt_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ empty_carrier(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& join_absorbing(X1)
& latt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> below_refl(X1,X2,X2) ),
inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices]) ).
fof(c_0_27,plain,
! [X7] :
( ( ~ empty_carrier(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( join_commutative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( join_associative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( meet_commutative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( meet_associative(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( meet_absorbing(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) )
& ( join_absorbing(X7)
| empty_carrier(X7)
| ~ lattice(X7)
| ~ latt_str(X7) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_28,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> relation_of_lattice(X1) = a_1_0_filter_1(X1) ),
inference(fof_simplification,[status(thm)],[d8_filter_1]) ).
fof(c_0_29,plain,
! [X55,X56] :
( ~ element(X55,X56)
| empty(X56)
| in(X55,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_30,plain,
( element(esk7_2(X1,X2),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_31,negated_conjecture,
( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),a_1_0_filter_1(esk12_0))
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_32,plain,
! [X50,X51,X52] :
( empty_carrier(X50)
| ~ meet_commutative(X50)
| ~ meet_absorbing(X50)
| ~ join_absorbing(X50)
| ~ latt_str(X50)
| ~ element(X51,the_carrier(X50))
| ~ element(X52,the_carrier(X50))
| below_refl(X50,X51,X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
cnf(c_0_33,plain,
( join_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( meet_absorbing(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
( meet_commutative(X1)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_36,plain,
! [X13] :
( empty_carrier(X13)
| ~ lattice(X13)
| ~ latt_str(X13)
| relation_of_lattice(X13) = a_1_0_filter_1(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
fof(c_0_37,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& element(X3,X1)
& element(X4,X2) )
=> ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_domain_1]) ).
cnf(c_0_38,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
( element(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0),the_carrier(esk12_0))
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_40,plain,
( empty_carrier(X1)
| below_refl(X1,X2,X2)
| ~ meet_commutative(X1)
| ~ meet_absorbing(X1)
| ~ join_absorbing(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_42,negated_conjecture,
join_absorbing(esk12_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_43,negated_conjecture,
meet_absorbing(esk12_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_44,negated_conjecture,
meet_commutative(esk12_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_45,plain,
( element(esk6_2(X1,X2),the_carrier(X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_46,plain,
( empty_carrier(X1)
| relation_of_lattice(X1) = a_1_0_filter_1(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_47,plain,
! [X43,X44,X45,X46] :
( empty(X43)
| empty(X44)
| ~ element(X45,X43)
| ~ element(X46,X44)
| ordered_pair_as_product_element(X43,X44,X45,X46) = ordered_pair(X45,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])]) ).
fof(c_0_48,plain,
! [X11,X12] : ordered_pair(X11,X12) = unordered_pair(unordered_pair(X11,X12),singleton(X11)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_49,plain,
! [X53,X54] :
( ~ in(X53,X54)
| element(X53,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_50,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0),the_carrier(esk12_0))
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_51,negated_conjecture,
( below_refl(esk12_0,X1,X1)
| ~ element(X1,the_carrier(esk12_0)) ),
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(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]),c_0_44]),c_0_24])]),c_0_25]) ).
fof(c_0_52,plain,
! [X26] : element(esk5_1(X26),X26),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_53,negated_conjecture,
( element(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0),the_carrier(esk12_0))
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_31]),c_0_23]),c_0_24])]),c_0_25]) ).
fof(c_0_54,plain,
! [X63,X64,X65,X66] :
( ( X63 = X65
| ordered_pair(X63,X64) != ordered_pair(X65,X66) )
& ( X64 = X66
| ordered_pair(X63,X64) != ordered_pair(X65,X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t33_zfmisc_1])])]) ).
cnf(c_0_55,negated_conjecture,
( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_56,negated_conjecture,
relation_of_lattice(esk12_0) = a_1_0_filter_1(esk12_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_57,negated_conjecture,
( ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),relation_of_lattice(esk12_0))
| ~ below_refl(esk12_0,esk13_0,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_58,plain,
( empty(X1)
| empty(X2)
| ordered_pair_as_product_element(X1,X2,X3,X4) = ordered_pair(X3,X4)
| ~ element(X3,X1)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_60,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_22])]) ).
cnf(c_0_62,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_63,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0),the_carrier(esk12_0))
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_53]) ).
cnf(c_0_64,plain,
( X1 = X2
| ordered_pair(X3,X1) != ordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_65,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_66,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),a_1_0_filter_1(esk12_0)) ),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,negated_conjecture,
( ~ below_refl(esk12_0,esk13_0,esk14_0)
| ~ in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),a_1_0_filter_1(esk12_0)) ),
inference(rw,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_68,negated_conjecture,
( in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk14_0),a_1_0_filter_1(esk12_0))
| ~ below_refl(esk12_0,X1,esk14_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_41]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_69,plain,
( X1 = X2
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_70,plain,
( ordered_pair_as_product_element(X1,X2,X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| empty(X2)
| empty(X1)
| ~ element(X4,X2)
| ~ element(X3,X1) ),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_71,negated_conjecture,
( element(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),the_carrier(esk12_0))
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_72,plain,
( below_refl(X1,esk6_2(X2,X1),esk7_2(X2,X1))
| empty_carrier(X1)
| ~ in(X2,a_1_0_filter_1(X1))
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_73,plain,
( below_refl(X1,X2,X2)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ join_absorbing(X1)
| ~ meet_absorbing(X1)
| ~ meet_commutative(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_62]) ).
cnf(c_0_74,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_51]),c_0_22])]) ).
cnf(c_0_75,plain,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),singleton(X3)) != unordered_pair(unordered_pair(X4,X2),singleton(X4)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_59]),c_0_59]) ).
cnf(c_0_76,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_77,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| element(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_66]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_78,negated_conjecture,
~ below_refl(esk12_0,esk13_0,esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_22])]) ).
cnf(c_0_79,plain,
( X1 = ordered_pair_as_product_element(the_carrier(X2),the_carrier(X2),esk6_2(X1,X2),esk7_2(X1,X2))
| empty_carrier(X2)
| ~ in(X1,a_1_0_filter_1(X2))
| ~ lattice(X2)
| ~ latt_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_80,plain,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),singleton(X1)) != unordered_pair(unordered_pair(X2,X4),singleton(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_59]),c_0_59]) ).
cnf(c_0_81,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk12_0),X2,esk13_0) = unordered_pair(unordered_pair(X2,esk13_0),singleton(X2))
| empty(the_carrier(esk12_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_82,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)),a_1_0_filter_1(esk12_0))
| ~ below_refl(esk12_0,X1,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0))
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_71]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_83,negated_conjecture,
( below_refl(esk12_0,esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0))
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_31]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_84,negated_conjecture,
below_refl(esk12_0,esk13_0,esk13_0),
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(spm,[status(thm)],[c_0_73,c_0_22]),c_0_42]),c_0_43]),c_0_44]),c_0_24])]),c_0_25]) ).
cnf(c_0_85,negated_conjecture,
( element(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),the_carrier(esk12_0))
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_74]) ).
cnf(c_0_86,plain,
( X1 = X2
| unordered_pair(unordered_pair(X3,X1),singleton(X3)) != unordered_pair(unordered_pair(X2,X4),singleton(X4)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk12_0),X2,esk14_0) = unordered_pair(unordered_pair(X2,esk14_0),singleton(X2))
| empty(the_carrier(esk12_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_41]) ).
cnf(c_0_88,negated_conjecture,
element(esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),the_carrier(esk12_0)),
inference(sr,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( below_refl(esk12_0,esk13_0,esk14_0)
| element(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_66]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_90,negated_conjecture,
( ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0)
| below_refl(esk12_0,esk13_0,esk14_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_66]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_91,plain,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),singleton(X1)) != unordered_pair(unordered_pair(X4,X2),singleton(X2)) ),
inference(spm,[status(thm)],[c_0_80,c_0_76]) ).
cnf(c_0_92,negated_conjecture,
( unordered_pair(unordered_pair(esk13_0,esk13_0),singleton(esk13_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_81,c_0_22]) ).
cnf(c_0_93,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)),a_1_0_filter_1(esk12_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_22])]),c_0_85]) ).
cnf(c_0_94,negated_conjecture,
( ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0),esk12_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),X1,esk13_0)
| ~ below_refl(esk12_0,X1,esk13_0)
| ~ element(X1,the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_31]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_95,plain,
( X1 = X2
| unordered_pair(singleton(X3),unordered_pair(X3,X1)) != unordered_pair(unordered_pair(X2,X4),singleton(X4)) ),
inference(spm,[status(thm)],[c_0_86,c_0_76]) ).
cnf(c_0_96,negated_conjecture,
( unordered_pair(unordered_pair(esk14_0,esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)),singleton(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0))) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_85]),c_0_76]) ).
cnf(c_0_97,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk12_0),X2,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) = unordered_pair(singleton(X2),unordered_pair(X2,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)))
| empty(the_carrier(esk12_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_88]),c_0_76]) ).
cnf(c_0_98,negated_conjecture,
element(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),the_carrier(esk12_0)),
inference(sr,[status(thm)],[c_0_89,c_0_78]) ).
cnf(c_0_99,negated_conjecture,
ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),
inference(sr,[status(thm)],[c_0_90,c_0_78]) ).
cnf(c_0_100,negated_conjecture,
( X1 = esk13_0
| empty(the_carrier(esk12_0))
| unordered_pair(unordered_pair(X1,X2),singleton(X1)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_101,negated_conjecture,
( ordered_pair_as_product_element(X1,the_carrier(esk12_0),X2,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)) = unordered_pair(singleton(X2),unordered_pair(X2,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)))
| empty(the_carrier(esk12_0))
| empty(X1)
| ~ element(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_76]) ).
cnf(c_0_102,negated_conjecture,
( empty(the_carrier(esk12_0))
| in(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),a_1_0_filter_1(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_84]),c_0_22])]) ).
cnf(c_0_103,plain,
( X1 = X2
| unordered_pair(unordered_pair(X1,X3),singleton(X1)) != unordered_pair(singleton(X2),unordered_pair(X2,X4)) ),
inference(spm,[status(thm)],[c_0_80,c_0_76]) ).
cnf(c_0_104,negated_conjecture,
( X1 = esk14_0
| empty(the_carrier(esk12_0))
| unordered_pair(singleton(X2),unordered_pair(X2,X1)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_105,negated_conjecture,
( unordered_pair(singleton(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)),unordered_pair(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( X1 = esk13_0
| empty(the_carrier(esk12_0))
| unordered_pair(singleton(X1),unordered_pair(X1,X2)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0) ),
inference(spm,[status(thm)],[c_0_100,c_0_76]) ).
cnf(c_0_107,negated_conjecture,
( unordered_pair(singleton(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)),unordered_pair(esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0))) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0))
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_101,c_0_85]) ).
cnf(c_0_108,negated_conjecture,
( ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0)) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0)
| empty(the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_102]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_109,plain,
( X1 = X2
| unordered_pair(singleton(X1),unordered_pair(X1,X3)) != unordered_pair(singleton(X2),unordered_pair(X2,X4)) ),
inference(spm,[status(thm)],[c_0_103,c_0_76]) ).
cnf(c_0_110,negated_conjecture,
( unordered_pair(singleton(esk13_0),unordered_pair(esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))) = ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_97,c_0_22]) ).
fof(c_0_111,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_112,plain,
! [X19] :
( ~ meet_semilatt_str(X19)
| one_sorted_str(X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_113,plain,
! [X21] :
( ( meet_semilatt_str(X21)
| ~ latt_str(X21) )
& ( join_semilatt_str(X21)
| ~ latt_str(X21) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_114,negated_conjecture,
( below_refl(esk12_0,esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0))
| below_refl(esk12_0,esk13_0,esk14_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_66]),c_0_23]),c_0_24])]),c_0_25]) ).
cnf(c_0_115,negated_conjecture,
( esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk14_0
| empty(the_carrier(esk12_0))
| ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0),esk14_0) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_116,negated_conjecture,
( esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk13_0),esk12_0) = esk13_0
| empty(the_carrier(esk12_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]) ).
cnf(c_0_117,negated_conjecture,
( X1 = esk13_0
| empty(the_carrier(esk12_0))
| unordered_pair(singleton(X1),unordered_pair(X1,X2)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
fof(c_0_118,plain,
! [X28] :
( empty_carrier(X28)
| ~ one_sorted_str(X28)
| ~ empty(the_carrier(X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])]) ).
cnf(c_0_119,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_120,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_121,negated_conjecture,
below_refl(esk12_0,esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)),
inference(sr,[status(thm)],[c_0_114,c_0_78]) ).
cnf(c_0_122,negated_conjecture,
( esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk14_0
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,negated_conjecture,
( esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk13_0
| empty(the_carrier(esk12_0))
| ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk7_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0)) != ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_105]) ).
cnf(c_0_124,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_125,plain,
( one_sorted_str(X1)
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_126,negated_conjecture,
( below_refl(esk12_0,esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0),esk14_0)
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_127,negated_conjecture,
( esk6_2(ordered_pair_as_product_element(the_carrier(esk12_0),the_carrier(esk12_0),esk13_0,esk14_0),esk12_0) = esk13_0
| empty(the_carrier(esk12_0)) ),
inference(spm,[status(thm)],[c_0_123,c_0_122]) ).
cnf(c_0_128,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ latt_str(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,negated_conjecture,
empty(the_carrier(esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_78]) ).
cnf(c_0_130,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_24])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU342+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
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 20:07:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 70.93/71.02 % Version : CSE_E---1.5
% 70.93/71.02 % Problem : theBenchmark.p
% 70.93/71.02 % Proof found
% 70.93/71.02 % SZS status Theorem for theBenchmark.p
% 70.93/71.02 % SZS output start Proof
% See solution above
% 71.04/71.03 % Total time : 70.446000 s
% 71.04/71.03 % SZS output end Proof
% 71.04/71.03 % Total time : 70.453000 s
%------------------------------------------------------------------------------