%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU343+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:47 PM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 82 ( 14 unt; 0 def)
% Number of atoms : 293 ( 70 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 363 ( 152 ~; 137 |; 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 : 157 ( 4 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_lattices,axiom,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(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/sandbox2/benchmark/theBenchmark.p',d2_lattices) ).
fof(d1_lattice3,axiom,
! [X1,X2] :
( ( latt_str(X2)
& strict_latt_str(X2) )
=> ( X2 = boole_lattice(X1)
<=> ( ! [X3] :
( element(X3,powerset(X1))
=> ! [X4] :
( element(X4,powerset(X1))
=> ( apply_binary(the_L_meet(X2),X3,X4) = subset_intersection2(X1,X3,X4)
& apply_binary(the_L_join(X2),X3,X4) = subset_union2(X1,X3,X4) ) ) )
& the_carrier(X2) = powerset(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( latt_str(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(fc1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& ~ empty_carrier(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& function(the_L_meet(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
fof(redefinition_k2_binop_1,axiom,
! [X1,X2,X3,X4,X5,X6] :
( ( element(X6,X2)
& element(X5,X1)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& function(X4)
& ~ empty(X2)
& ~ empty(X1) )
=> apply_binary_as_element(X1,X2,X3,X4,X5,X6) = apply_binary(X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(d1_lattices,axiom,
! [X1] :
( ( join_semilatt_str(X1)
& ~ empty_carrier(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/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& function(the_L_join(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.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)))
=> ( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
& join(boole_lattice(X1),X2,X3) = set_union2(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
fof(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( join_semilatt_str(X1)
& meet_semilatt_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(redefinition_k5_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X3,powerset(X1))
& element(X2,powerset(X1)) )
=> subset_intersection2(X1,X2,X3) = set_intersection2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X3,powerset(X1))
& element(X2,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(c_0_14,plain,
! [X1] :
( ( meet_semilatt_str(X1)
& ~ empty_carrier(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] :
( ( ~ latt_str(X24)
| ~ strict_latt_str(X24)
| X24 = boole_lattice(X23)
| the_carrier(X24) != powerset(X23)
| 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))
| 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)) )
& ( ~ latt_str(X24)
| ~ strict_latt_str(X24)
| X24 = boole_lattice(X23)
| the_carrier(X24) != powerset(X23)
| element(esk5_2(X23,X24),powerset(X23)) )
& ( ~ latt_str(X24)
| ~ strict_latt_str(X24)
| X24 = boole_lattice(X23)
| the_carrier(X24) != powerset(X23)
| element(esk4_2(X23,X24),powerset(X23)) )
& ( ~ latt_str(X24)
| ~ strict_latt_str(X24)
| X24 != boole_lattice(X23)
| ~ element(X25,powerset(X23))
| ~ element(X26,powerset(X23))
| apply_binary(the_L_meet(X24),X25,X26) = subset_intersection2(X23,X25,X26) )
& ( ~ latt_str(X24)
| ~ strict_latt_str(X24)
| X24 != boole_lattice(X23)
| ~ element(X25,powerset(X23))
| ~ element(X26,powerset(X23))
| apply_binary(the_L_join(X24),X25,X26) = subset_union2(X23,X25,X26) )
& ( ~ latt_str(X24)
| ~ strict_latt_str(X24)
| X24 != boole_lattice(X23)
| the_carrier(X24) = powerset(X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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] :
( latt_str(boole_lattice(X29))
& strict_latt_str(boole_lattice(X29)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_17,plain,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& ~ empty_carrier(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_18,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(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])])]) ).
fof(c_0_19,plain,
! [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)
| quasi_total(the_L_meet(X78),cartesian_product2(the_carrier(X78),the_carrier(X78)),the_carrier(X78)) )
& ( ~ meet_semilatt_str(X78)
| function(the_L_meet(X78)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])])]) ).
fof(c_0_20,plain,
! [X17,X18,X19] :
( meet(X17,X18,X19) = apply_binary_as_element(the_carrier(X17),the_carrier(X17),the_carrier(X17),the_L_meet(X17),X18,X19)
| ~ element(X19,the_carrier(X17))
| ~ element(X18,the_carrier(X17))
| ~ meet_semilatt_str(X17)
| empty_carrier(X17) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_21,plain,
( ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X2)
| the_carrier(X1) = powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_24,plain,
! [X30] :
( strict_latt_str(boole_lattice(X30))
& ~ empty_carrier(boole_lattice(X30)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_17])]) ).
fof(c_0_25,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( element(X6,X2)
& element(X5,X1)
& relation_of2(X4,cartesian_product2(X1,X2),X3)
& quasi_total(X4,cartesian_product2(X1,X2),X3)
& function(X4)
& ~ empty(X2)
& ~ empty(X1) )
=> 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_26,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_27,plain,
( ~ relation_of2_as_subset(X1,X2,X3)
| relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( ~ meet_semilatt_str(X1)
| relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_29,plain,
! [X1] :
( ( join_semilatt_str(X1)
& ~ empty_carrier(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_30,plain,
! [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)
| quasi_total(the_L_join(X92),cartesian_product2(the_carrier(X92),the_carrier(X92)),the_carrier(X92)) )
& ( ~ join_semilatt_str(X92)
| function(the_L_join(X92)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])])]) ).
cnf(c_0_31,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| meet(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_meet(X1),X2,X3)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,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_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_33,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_34,plain,
! [X71,X72,X73,X74,X75,X76] :
( apply_binary_as_element(X71,X72,X73,X74,X75,X76) = apply_binary(X74,X75,X76)
| ~ element(X76,X72)
| ~ element(X75,X71)
| ~ relation_of2(X74,cartesian_product2(X71,X72),X73)
| ~ quasi_total(X74,cartesian_product2(X71,X72),X73)
| ~ function(X74)
| empty(X72)
| empty(X71) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_35,plain,
! [X62] : ~ empty(powerset(X62)),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
cnf(c_0_36,plain,
( ~ meet_semilatt_str(X1)
| quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,plain,
( ~ meet_semilatt_str(X1)
| relation_of2(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_38,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3)
& join(boole_lattice(X1),X2,X3) = set_union2(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t1_lattice3]) ).
fof(c_0_39,plain,
! [X41,X42,X43] :
( join(X41,X42,X43) = apply_binary_as_element(the_carrier(X41),the_carrier(X41),the_carrier(X41),the_L_join(X41),X42,X43)
| ~ element(X43,the_carrier(X41))
| ~ element(X42,the_carrier(X41))
| ~ join_semilatt_str(X41)
| empty_carrier(X41) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
cnf(c_0_40,plain,
( ~ join_semilatt_str(X1)
| relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,plain,
( ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X4)
| ~ element(X2,powerset(X4))
| ~ element(X3,powerset(X4))
| apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_42,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1))
| apply_binary_as_element(powerset(X1),powerset(X1),powerset(X1),the_L_meet(boole_lattice(X1)),X2,X3) = meet(boole_lattice(X1),X2,X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_43,plain,
( ~ element(X6,X2)
| ~ element(X5,X1)
| ~ relation_of2(X3,cartesian_product2(X1,X2),X4)
| ~ quasi_total(X3,cartesian_product2(X1,X2),X4)
| ~ function(X3)
| apply_binary_as_element(X1,X2,X4,X3,X5,X6) = apply_binary(X3,X5,X6)
| empty(X2)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( ~ meet_semilatt_str(X1)
| function(the_L_meet(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_46,plain,
( ~ meet_semilatt_str(boole_lattice(X1))
| quasi_total(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_47,plain,
( ~ meet_semilatt_str(boole_lattice(X1))
| relation_of2(the_L_meet(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
fof(c_0_48,negated_conjecture,
( ( meet(boole_lattice(esk1_0),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0) )
& element(esk3_0,the_carrier(boole_lattice(esk1_0)))
& element(esk2_0,the_carrier(boole_lattice(esk1_0))) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])]) ).
cnf(c_0_49,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
( ~ join_semilatt_str(X1)
| quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_51,plain,
( ~ join_semilatt_str(X1)
| relation_of2(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_52,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = subset_intersection2(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_22]),c_0_23])]) ).
cnf(c_0_53,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1))
| apply_binary(the_L_meet(boole_lattice(X1)),X2,X3) = meet(boole_lattice(X1),X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_54,negated_conjecture,
element(esk3_0,the_carrier(boole_lattice(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
element(esk2_0,the_carrier(boole_lattice(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
( ~ latt_str(X1)
| ~ strict_latt_str(X1)
| X1 != boole_lattice(X4)
| ~ element(X2,powerset(X4))
| ~ element(X3,powerset(X4))
| apply_binary(the_L_join(X1),X2,X3) = subset_union2(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_57,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1))
| apply_binary_as_element(powerset(X1),powerset(X1),powerset(X1),the_L_join(boole_lattice(X1)),X2,X3) = join(boole_lattice(X1),X2,X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_32]),c_0_33]) ).
cnf(c_0_58,plain,
( ~ join_semilatt_str(X1)
| function(the_L_join(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_59,plain,
( ~ join_semilatt_str(boole_lattice(X1))
| quasi_total(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_32]) ).
cnf(c_0_60,plain,
( ~ join_semilatt_str(boole_lattice(X1))
| relation_of2(the_L_join(boole_lattice(X1)),cartesian_product2(powerset(X1),powerset(X1)),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_32]) ).
cnf(c_0_61,negated_conjecture,
( meet(boole_lattice(esk1_0),esk2_0,esk3_0) != set_intersection2(esk2_0,esk3_0)
| join(boole_lattice(esk1_0),esk2_0,esk3_0) != set_union2(esk2_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_62,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| ~ meet_semilatt_str(boole_lattice(X1))
| meet(boole_lattice(X1),X2,X3) = subset_intersection2(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
element(esk3_0,powerset(esk1_0)),
inference(rw,[status(thm)],[c_0_54,c_0_32]) ).
cnf(c_0_64,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(rw,[status(thm)],[c_0_55,c_0_32]) ).
cnf(c_0_65,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = subset_union2(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_56]),c_0_22]),c_0_23])]) ).
cnf(c_0_66,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1))
| apply_binary(the_L_join(boole_lattice(X1)),X2,X3) = join(boole_lattice(X1),X2,X3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_43]),c_0_44]),c_0_58]),c_0_59]),c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( ~ meet_semilatt_str(boole_lattice(esk1_0))
| set_intersection2(esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0)
| join(boole_lattice(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(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_64])]) ).
cnf(c_0_68,plain,
( ~ element(X2,powerset(X1))
| ~ element(X3,powerset(X1))
| ~ join_semilatt_str(boole_lattice(X1))
| join(boole_lattice(X1),X2,X3) = subset_union2(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
fof(c_0_69,plain,
! [X80] :
( ( ~ latt_str(X80)
| join_semilatt_str(X80) )
& ( ~ latt_str(X80)
| meet_semilatt_str(X80) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ join_semilatt_str(boole_lattice(esk1_0))
| ~ meet_semilatt_str(boole_lattice(esk1_0))
| set_intersection2(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) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_63]),c_0_64])]) ).
cnf(c_0_71,plain,
( ~ latt_str(X1)
| meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( ~ join_semilatt_str(boole_lattice(esk1_0))
| set_intersection2(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) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_23])]) ).
cnf(c_0_73,plain,
( ~ latt_str(X1)
| join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
fof(c_0_74,plain,
! [X13,X14,X15] :
( subset_intersection2(X13,X14,X15) = set_intersection2(X14,X15)
| ~ element(X15,powerset(X13))
| ~ element(X14,powerset(X13)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])])]) ).
cnf(c_0_75,negated_conjecture,
( set_intersection2(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) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_23])]) ).
cnf(c_0_76,plain,
( ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2))
| subset_intersection2(X2,X1,X3) = set_intersection2(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( ~ element(esk2_0,powerset(X1))
| ~ element(esk3_0,powerset(X1))
| subset_union2(esk1_0,esk2_0,esk3_0) != set_union2(esk2_0,esk3_0)
| subset_intersection2(X1,esk2_0,esk3_0) != subset_intersection2(esk1_0,esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
fof(c_0_78,plain,
! [X38,X39,X40] :
( subset_union2(X38,X39,X40) = set_union2(X39,X40)
| ~ element(X40,powerset(X38))
| ~ element(X39,powerset(X38)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])])]) ).
cnf(c_0_79,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_77]),c_0_63]),c_0_64])]) ).
cnf(c_0_80,plain,
( ~ element(X3,powerset(X2))
| ~ element(X1,powerset(X2))
| subset_union2(X2,X1,X3) = set_union2(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_63]),c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU343+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 06:13:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 % Version: 3.5.1
% 0.19/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.19/0.51 % Starting sh5l with 300s (1) cores
% 0.19/0.51 % new_bool_3 with pid 2421430 completed with status 0
% 0.19/0.51 % Result found by new_bool_3
% 0.19/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.51 % Search class: FGHSM-FFMM32-SFFFFFNN
% 0.19/0.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.51 % SubtermCWHack with pid 2421433 completed with status 0
% 0.19/0.51 % Result found by SubtermCWHack
% 0.19/0.51 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.51 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.19/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.51 % Search class: FGHSM-FFMM32-SFFFFFNN
% 0.19/0.51 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.51 % Starting SubtermCWHack with 28s (1) cores
% 0.19/0.51 % Preprocessing time : 0.002 s
% 0.19/0.51
% 0.19/0.51 % Proof found!
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
% 0.19/0.51 % Parsed axioms : 86
% 0.19/0.51 % Removed by relevancy pruning/SinE : 28
% 0.19/0.51 % Initial clauses : 84
% 0.19/0.51 % Removed in clause preprocessing : 0
% 0.19/0.51 % Initial clauses in saturation : 84
% 0.19/0.51 % Processed clauses : 507
% 0.19/0.51 % ...of these trivial : 5
% 0.19/0.51 % ...subsumed : 229
% 0.19/0.51 % ...remaining for further processing : 273
% 0.19/0.51 % Other redundant clauses eliminated : 16
% 0.19/0.51 % Clauses deleted for lack of memory : 0
% 0.19/0.51 % Backward-subsumed : 6
% 0.19/0.51 % Backward-rewritten : 5
% 0.19/0.51 % Generated clauses : 2296
% 0.19/0.51 % ...of the previous two non-redundant : 2222
% 0.19/0.51 % ...aggressively subsumed : 0
% 0.19/0.51 % Contextual simplify-reflections : 108
% 0.19/0.51 % Paramodulations : 2266
% 0.19/0.51 % Factorizations : 0
% 0.19/0.51 % NegExts : 0
% 0.19/0.51 % Equation resolutions : 30
% 0.19/0.51 % Disequality decompositions : 0
% 0.19/0.51 % Total rewrite steps : 148
% 0.19/0.51 % ...of those cached : 123
% 0.19/0.51 % Propositional unsat checks : 0
% 0.19/0.51 % Propositional check models : 0
% 0.19/0.51 % Propositional check unsatisfiable : 0
% 0.19/0.51 % Propositional clauses : 0
% 0.19/0.51 % Propositional clauses after purity: 0
% 0.19/0.51 % Propositional unsat core size : 0
% 0.19/0.51 % Propositional preprocessing time : 0.000
% 0.19/0.51 % Propositional encoding time : 0.000
% 0.19/0.51 % Propositional solver time : 0.000
% 0.19/0.51 % Success case prop preproc time : 0.000
% 0.19/0.51 % Success case prop encoding time : 0.000
% 0.19/0.51 % Success case prop solver time : 0.000
% 0.19/0.51 % Current number of processed clauses : 259
% 0.19/0.51 % Positive orientable unit clauses : 30
% 0.19/0.51 % Positive unorientable unit clauses: 2
% 0.19/0.51 % Negative unit clauses : 8
% 0.19/0.51 % Non-unit-clauses : 219
% 0.19/0.51 % Current number of unprocessed clauses: 1781
% 0.19/0.51 % ...number of literals in the above : 8600
% 0.19/0.51 % Current number of archived formulas : 0
% 0.19/0.51 % Current number of archived clauses : 11
% 0.19/0.51 % Clause-clause subsumption calls (NU) : 12029
% 0.19/0.51 % Rec. Clause-clause subsumption calls : 5555
% 0.19/0.51 % Non-unit clause-clause subsumptions : 336
% 0.19/0.51 % Unit Clause-clause subsumption calls : 60
% 0.19/0.51 % Rewrite failures with RHS unbound : 0
% 0.19/0.51 % BW rewrite match attempts : 18
% 0.19/0.51 % BW rewrite match successes : 16
% 0.19/0.51 % Condensation attempts : 0
% 0.19/0.51 % Condensation successes : 0
% 0.19/0.51 % Termbank termtop insertions : 92015
% 0.19/0.51 % Search garbage collected termcells : 1137
% 0.19/0.51
% 0.19/0.51 % -------------------------------------------------
% 0.19/0.51 % User time : 0.067 s
% 0.19/0.51 % System time : 0.006 s
% 0.19/0.51 % Total time : 0.072 s
% 0.19/0.51 % Maximum resident set size: 3972 pages
% 0.19/0.51
% 0.19/0.51 % -------------------------------------------------
% 0.19/0.51 % User time : 0.071 s
% 0.19/0.51 % System time : 0.009 s
% 0.19/0.51 % Total time : 0.080 s
% 0.19/0.51 % Maximum resident set size: 4608 pages
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------