TSTP Solution File: SEU343+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:26:04 EDT 2023
% Result : Theorem 0.45s 0.56s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 86 ( 14 unt; 0 def)
% Number of atoms : 315 ( 74 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 399 ( 170 ~; 155 |; 46 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-6 aty)
% Number of variables : 169 ( 4 sgn; 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',d2_lattices) ).
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',d1_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',dt_k1_lattice3) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',fc1_lattice3) ).
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',redefinition_k2_binop_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',fc1_subset_1) ).
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',d1_lattices) ).
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',dt_u1_lattices) ).
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',redefinition_m2_relset_1) ).
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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',dt_u2_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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',t1_lattice3) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',dt_l3_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/tmp/tmp.RV1Cp63ext/E---3.1_21755.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/tmp/tmp.RV1Cp63ext/E---3.1_21755.p',redefinition_k4_subset_1) ).
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,
! [X23,X24,X25,X26] :
( ( the_carrier(X24) = powerset(X23)
| X24 != boole_lattice(X23)
| ~ strict_latt_str(X24)
| ~ latt_str(X24) )
& ( apply_binary(the_L_join(X24),X25,X26) = subset_union2(X23,X25,X26)
| ~ element(X26,powerset(X23))
| ~ element(X25,powerset(X23))
| X24 != boole_lattice(X23)
| ~ strict_latt_str(X24)
| ~ latt_str(X24) )
& ( apply_binary(the_L_meet(X24),X25,X26) = subset_intersection2(X23,X25,X26)
| ~ element(X26,powerset(X23))
| ~ element(X25,powerset(X23))
| X24 != boole_lattice(X23)
| ~ strict_latt_str(X24)
| ~ latt_str(X24) )
& ( element(esk4_2(X23,X24),powerset(X23))
| the_carrier(X24) != powerset(X23)
| X24 = boole_lattice(X23)
| ~ strict_latt_str(X24)
| ~ latt_str(X24) )
& ( element(esk5_2(X23,X24),powerset(X23))
| the_carrier(X24) != powerset(X23)
| X24 = boole_lattice(X23)
| ~ strict_latt_str(X24)
| ~ latt_str(X24) )
& ( apply_binary(the_L_join(X24),esk4_2(X23,X24),esk5_2(X23,X24)) != subset_union2(X23,esk4_2(X23,X24),esk5_2(X23,X24))
| apply_binary(the_L_meet(X24),esk4_2(X23,X24),esk5_2(X23,X24)) != subset_intersection2(X23,esk4_2(X23,X24),esk5_2(X23,X24))
| the_carrier(X24) != powerset(X23)
| X24 = boole_lattice(X23)
| ~ strict_latt_str(X24)
| ~ latt_str(X24) ) ),
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_16,plain,
! [X29] :
( strict_latt_str(boole_lattice(X29))
& latt_str(boole_lattice(X29)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_17,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_18,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_19,plain,
! [X17,X18,X19] :
( empty_carrier(X17)
| ~ meet_semilatt_str(X17)
| ~ element(X18,the_carrier(X17))
| ~ element(X19,the_carrier(X17))
| meet(X17,X18,X19) = apply_binary_as_element(the_carrier(X17),the_carrier(X17),the_carrier(X17),the_L_meet(X17),X18,X19) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_20,plain,
( the_carrier(X1) = powerset(X2)
| X1 != boole_lattice(X2)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X30] :
( ~ empty_carrier(boole_lattice(X30))
& strict_latt_str(boole_lattice(X30)) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
fof(c_0_24,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(c_0_25,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_26,plain,
! [X71,X72,X73,X74,X75,X76] :
( empty(X71)
| empty(X72)
| ~ function(X74)
| ~ quasi_total(X74,cartesian_product2(X71,X72),X73)
| ~ relation_of2(X74,cartesian_product2(X71,X72),X73)
| ~ element(X75,X71)
| ~ element(X76,X72)
| apply_binary_as_element(X71,X72,X73,X74,X75,X76) = apply_binary(X74,X75,X76) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_27,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_19]) ).
cnf(c_0_28,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_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_29,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X62] : ~ empty(powerset(X62)),
inference(variable_rename,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X78] :
( ( function(the_L_meet(X78))
| ~ meet_semilatt_str(X78) )
& ( quasi_total(the_L_meet(X78),cartesian_product2(the_carrier(X78),the_carrier(X78)),the_carrier(X78))
| ~ meet_semilatt_str(X78) )
& ( relation_of2_as_subset(the_L_meet(X78),cartesian_product2(the_carrier(X78),the_carrier(X78)),the_carrier(X78))
| ~ meet_semilatt_str(X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(c_0_32,plain,
! [X104,X105,X106] :
( ( ~ relation_of2_as_subset(X106,X104,X105)
| relation_of2(X106,X104,X105) )
& ( ~ relation_of2(X106,X104,X105)
| relation_of2_as_subset(X106,X104,X105) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_33,plain,
! [X41,X42,X43] :
( empty_carrier(X41)
| ~ join_semilatt_str(X41)
| ~ element(X42,the_carrier(X41))
| ~ element(X43,the_carrier(X41))
| join(X41,X42,X43) = apply_binary_as_element(the_carrier(X41),the_carrier(X41),the_carrier(X41),the_L_join(X41),X42,X43) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
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_26]) ).
cnf(c_0_35,plain,
( apply_binary_as_element(powerset(X1),powerset(X1),powerset(X1),the_L_meet(boole_lattice(X1)),X2,X3) = meet(boole_lattice(X1),X2,X3)
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_36,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,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_31]) ).
cnf(c_0_39,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,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_31]) ).
cnf(c_0_41,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_33]) ).
fof(c_0_42,plain,
! [X92] :
( ( function(the_L_join(X92))
| ~ join_semilatt_str(X92) )
& ( quasi_total(the_L_join(X92),cartesian_product2(the_carrier(X92),the_carrier(X92)),the_carrier(X92))
| ~ join_semilatt_str(X92) )
& ( relation_of2_as_subset(the_L_join(X92),cartesian_product2(the_carrier(X92),the_carrier(X92)),the_carrier(X92))
| ~ join_semilatt_str(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
cnf(c_0_43,plain,
( apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = meet(boole_lattice(X1),X2,X3)
| ~ relation_of2(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ quasi_total(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_44,plain,
( quasi_total(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_45,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_39,c_0_40]) ).
fof(c_0_46,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]) ).
cnf(c_0_47,plain,
( apply_binary_as_element(powerset(X1),powerset(X1),powerset(X1),the_L_join(boole_lattice(X1)),X2,X3) = join(boole_lattice(X1),X2,X3)
| ~ join_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_28]),c_0_29]) ).
cnf(c_0_48,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_49,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_42]) ).
cnf(c_0_50,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_42]) ).
cnf(c_0_51,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_15]) ).
cnf(c_0_52,plain,
( apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = meet(boole_lattice(X1),X2,X3)
| ~ relation_of2(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
( relation_of2(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_28]) ).
fof(c_0_54,negated_conjecture,
( element(esk2_0,the_carrier(boole_lattice(esk1_0)))
& element(esk3_0,the_carrier(boole_lattice(esk1_0)))
& ( join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| meet(boole_lattice(esk1_0),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
cnf(c_0_55,plain,
( apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = join(boole_lattice(X1),X2,X3)
| ~ relation_of2(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ quasi_total(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_36]),c_0_48]) ).
cnf(c_0_56,plain,
( quasi_total(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_28]) ).
cnf(c_0_57,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_39,c_0_50]) ).
cnf(c_0_58,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_51]),c_0_21]),c_0_22])]) ).
cnf(c_0_59,plain,
( apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = meet(boole_lattice(X1),X2,X3)
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
element(esk3_0,the_carrier(boole_lattice(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
element(esk2_0,the_carrier(boole_lattice(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,plain,
( apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = join(boole_lattice(X1),X2,X3)
| ~ relation_of2(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
( relation_of2(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_28]) ).
cnf(c_0_64,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_15]) ).
cnf(c_0_65,negated_conjecture,
( join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| meet(boole_lattice(esk1_0),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,plain,
( meet(boole_lattice(X1),X2,X3) = subset_intersection2(X1,X2,X3)
| ~ meet_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
element(esk3_0,powerset(esk1_0)),
inference(rw,[status(thm)],[c_0_60,c_0_28]) ).
cnf(c_0_68,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(rw,[status(thm)],[c_0_61,c_0_28]) ).
cnf(c_0_69,plain,
( apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = join(boole_lattice(X1),X2,X3)
| ~ join_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,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_64]),c_0_21]),c_0_22])]) ).
cnf(c_0_71,negated_conjecture,
( join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_72,plain,
( join(boole_lattice(X1),X2,X3) = subset_union2(X1,X2,X3)
| ~ join_semilatt_str(boole_lattice(X1))
| ~ element(X3,powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_73,plain,
! [X80] :
( ( meet_semilatt_str(X80)
| ~ latt_str(X80) )
& ( join_semilatt_str(X80)
| ~ latt_str(X80) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_74,negated_conjecture,
( subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_67]),c_0_68])]) ).
cnf(c_0_75,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_76,negated_conjecture,
( subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| ~ join_semilatt_str(boole_lattice(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_22])]) ).
cnf(c_0_77,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
fof(c_0_78,plain,
! [X13,X14,X15] :
( ~ element(X14,powerset(X13))
| ~ element(X15,powerset(X13))
| subset_intersection2(X13,X14,X15) = set_intersection2(X14,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
cnf(c_0_79,negated_conjecture,
( subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_22])]) ).
cnf(c_0_80,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_78]) ).
cnf(c_0_81,negated_conjecture,
( subset_intersection2(X1,esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| ~ element(esk3_0,powerset(X1))
| ~ element(esk2_0,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_82,plain,
! [X38,X39,X40] :
( ~ element(X39,powerset(X38))
| ~ element(X40,powerset(X38))
| subset_union2(X38,X39,X40) = set_union2(X39,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_83,negated_conjecture,
subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_81]),c_0_67]),c_0_68])]) ).
cnf(c_0_84,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_82]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_67]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU343+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 2400
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Oct 2 09:11:39 EDT 2023
% 0.23/0.36 % CPUTime :
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.RV1Cp63ext/E---3.1_21755.p
% 0.45/0.56 # Version: 3.1pre001
% 0.45/0.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.45/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.45/0.56 # Starting new_bool_3 with 300s (1) cores
% 0.45/0.56 # Starting new_bool_1 with 300s (1) cores
% 0.45/0.56 # Starting sh5l with 300s (1) cores
% 0.45/0.56 # new_bool_3 with pid 21911 completed with status 0
% 0.45/0.56 # Result found by new_bool_3
% 0.45/0.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.45/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.45/0.56 # Starting new_bool_3 with 300s (1) cores
% 0.45/0.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.45/0.56 # Search class: FGHSM-FFMM32-SFFFFFNN
% 0.45/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.45/0.56 # Starting G-E--_301_C18_F1_URBAN_S0Y with 139s (1) cores
% 0.45/0.56 # G-E--_301_C18_F1_URBAN_S0Y with pid 21923 completed with status 0
% 0.45/0.56 # Result found by G-E--_301_C18_F1_URBAN_S0Y
% 0.45/0.56 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.45/0.56 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.56 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.45/0.56 # Starting new_bool_3 with 300s (1) cores
% 0.45/0.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.45/0.56 # Search class: FGHSM-FFMM32-SFFFFFNN
% 0.45/0.56 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.45/0.56 # Starting G-E--_301_C18_F1_URBAN_S0Y with 139s (1) cores
% 0.45/0.56 # Preprocessing time : 0.008 s
% 0.45/0.56
% 0.45/0.56 # Proof found!
% 0.45/0.56 # SZS status Theorem
% 0.45/0.56 # SZS output start CNFRefutation
% See solution above
% 0.45/0.56 # Parsed axioms : 86
% 0.45/0.56 # Removed by relevancy pruning/SinE : 28
% 0.45/0.56 # Initial clauses : 84
% 0.45/0.56 # Removed in clause preprocessing : 0
% 0.45/0.56 # Initial clauses in saturation : 84
% 0.45/0.56 # Processed clauses : 255
% 0.45/0.56 # ...of these trivial : 5
% 0.45/0.56 # ...subsumed : 76
% 0.45/0.56 # ...remaining for further processing : 174
% 0.45/0.56 # Other redundant clauses eliminated : 0
% 0.45/0.56 # Clauses deleted for lack of memory : 0
% 0.45/0.56 # Backward-subsumed : 20
% 0.45/0.56 # Backward-rewritten : 7
% 0.45/0.56 # Generated clauses : 339
% 0.45/0.56 # ...of the previous two non-redundant : 301
% 0.45/0.56 # ...aggressively subsumed : 0
% 0.45/0.56 # Contextual simplify-reflections : 33
% 0.45/0.56 # Paramodulations : 335
% 0.45/0.56 # Factorizations : 0
% 0.45/0.56 # NegExts : 0
% 0.45/0.56 # Equation resolutions : 4
% 0.45/0.56 # Total rewrite steps : 118
% 0.45/0.56 # Propositional unsat checks : 0
% 0.45/0.56 # Propositional check models : 0
% 0.45/0.56 # Propositional check unsatisfiable : 0
% 0.45/0.56 # Propositional clauses : 0
% 0.45/0.56 # Propositional clauses after purity: 0
% 0.45/0.56 # Propositional unsat core size : 0
% 0.45/0.56 # Propositional preprocessing time : 0.000
% 0.45/0.56 # Propositional encoding time : 0.000
% 0.45/0.56 # Propositional solver time : 0.000
% 0.45/0.56 # Success case prop preproc time : 0.000
% 0.45/0.56 # Success case prop encoding time : 0.000
% 0.45/0.56 # Success case prop solver time : 0.000
% 0.45/0.56 # Current number of processed clauses : 147
% 0.45/0.56 # Positive orientable unit clauses : 30
% 0.45/0.56 # Positive unorientable unit clauses: 2
% 0.45/0.56 # Negative unit clauses : 8
% 0.45/0.56 # Non-unit-clauses : 107
% 0.45/0.56 # Current number of unprocessed clauses: 96
% 0.45/0.56 # ...number of literals in the above : 566
% 0.45/0.56 # Current number of archived formulas : 0
% 0.45/0.56 # Current number of archived clauses : 27
% 0.45/0.56 # Clause-clause subsumption calls (NU) : 4883
% 0.45/0.56 # Rec. Clause-clause subsumption calls : 1591
% 0.45/0.56 # Non-unit clause-clause subsumptions : 124
% 0.45/0.56 # Unit Clause-clause subsumption calls : 407
% 0.45/0.56 # Rewrite failures with RHS unbound : 0
% 0.45/0.56 # BW rewrite match attempts : 23
% 0.45/0.56 # BW rewrite match successes : 20
% 0.45/0.56 # Condensation attempts : 0
% 0.45/0.56 # Condensation successes : 0
% 0.45/0.56 # Termbank termtop insertions : 13493
% 0.45/0.56
% 0.45/0.56 # -------------------------------------------------
% 0.45/0.56 # User time : 0.029 s
% 0.45/0.56 # System time : 0.009 s
% 0.45/0.56 # Total time : 0.038 s
% 0.45/0.56 # Maximum resident set size: 2080 pages
% 0.45/0.56
% 0.45/0.56 # -------------------------------------------------
% 0.45/0.56 # User time : 0.032 s
% 0.45/0.56 # System time : 0.011 s
% 0.45/0.56 # Total time : 0.043 s
% 0.45/0.56 # Maximum resident set size: 1760 pages
% 0.45/0.56 % E---3.1 exiting
% 0.45/0.56 % E---3.1 exiting
%------------------------------------------------------------------------------