%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU343+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.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 : Tue May 5 05:11:32 PM UTC 2026
% Result : Theorem 3.90s 3.15s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 10 unt; 0 def)
% Number of atoms : 305 ( 68 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 375 ( 154 ~; 141 |; 48 &)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-6 aty)
% Number of variables : 155 ( 3 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
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/sandbox2/benchmark/theBenchmark.p',d2_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/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(dt_u1_lattices,axiom,
! [X1] :
( meet_semilatt_str(X1)
=> ( function(the_L_meet(X1))
& quasi_total(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_meet(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_lattices) ).
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(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/sandbox2/benchmark/theBenchmark.p',d1_lattice3) ).
fof(dt_k1_lattice3,axiom,
! [X1] :
( strict_latt_str(boole_lattice(X1))
& latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(fc1_lattice3,axiom,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
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/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
fof(d1_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,X2,X3) = apply_binary_as_element(the_carrier(X1),the_carrier(X1),the_carrier(X1),the_L_join(X1),X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattices) ).
fof(dt_u2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> ( function(the_L_join(X1))
& quasi_total(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1))
& relation_of2_as_subset(the_L_join(X1),cartesian_product2(the_carrier(X1),the_carrier(X1)),the_carrier(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(dt_l2_lattices,axiom,
! [X1] :
( join_semilatt_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_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(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/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
fof(redefinition_k4_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(c_0_16,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_17,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_18,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_19,plain,
! [X292,X293,X294] :
( ( ~ relation_of2_as_subset(X294,X292,X293)
| relation_of2(X294,X292,X293) )
& ( ~ relation_of2(X294,X292,X293)
| relation_of2_as_subset(X294,X292,X293) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_20,plain,
! [X226] :
( ( function(the_L_meet(X226))
| ~ meet_semilatt_str(X226) )
& ( quasi_total(the_L_meet(X226),cartesian_product2(the_carrier(X226),the_carrier(X226)),the_carrier(X226))
| ~ meet_semilatt_str(X226) )
& ( relation_of2_as_subset(the_L_meet(X226),cartesian_product2(the_carrier(X226),the_carrier(X226)),the_carrier(X226))
| ~ meet_semilatt_str(X226) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_lattices])])]) ).
fof(c_0_21,plain,
! [X241] :
( empty_carrier(X241)
| ~ one_sorted_str(X241)
| ~ empty(the_carrier(X241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])]) ).
fof(c_0_22,plain,
! [X220] :
( ~ meet_semilatt_str(X220)
| one_sorted_str(X220) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_lattices])]) ).
fof(c_0_23,plain,
! [X280,X281,X282,X283,X284,X285] :
( empty(X280)
| empty(X281)
| ~ function(X283)
| ~ quasi_total(X283,cartesian_product2(X280,X281),X282)
| ~ relation_of2(X283,cartesian_product2(X280,X281),X282)
| ~ element(X284,X280)
| ~ element(X285,X281)
| apply_binary_as_element(X280,X281,X282,X283,X284,X285) = apply_binary(X283,X284,X285) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
fof(c_0_24,plain,
! [X193,X194,X195] :
( empty_carrier(X193)
| ~ meet_semilatt_str(X193)
| ~ element(X194,the_carrier(X193))
| ~ element(X195,the_carrier(X193))
| meet(X193,X194,X195) = apply_binary_as_element(the_carrier(X193),the_carrier(X193),the_carrier(X193),the_L_meet(X193),X194,X195) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_25,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,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_20]) ).
cnf(c_0_27,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( one_sorted_str(X1)
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X184,X185,X186,X187] :
( ( the_carrier(X185) = powerset(X184)
| X185 != boole_lattice(X184)
| ~ strict_latt_str(X185)
| ~ latt_str(X185) )
& ( apply_binary(the_L_join(X185),X186,X187) = subset_union2(X184,X186,X187)
| ~ element(X187,powerset(X184))
| ~ element(X186,powerset(X184))
| X185 != boole_lattice(X184)
| ~ strict_latt_str(X185)
| ~ latt_str(X185) )
& ( apply_binary(the_L_meet(X185),X186,X187) = subset_intersection2(X184,X186,X187)
| ~ element(X187,powerset(X184))
| ~ element(X186,powerset(X184))
| X185 != boole_lattice(X184)
| ~ strict_latt_str(X185)
| ~ latt_str(X185) )
& ( element(esk1_2(X184,X185),powerset(X184))
| the_carrier(X185) != powerset(X184)
| X185 = boole_lattice(X184)
| ~ strict_latt_str(X185)
| ~ latt_str(X185) )
& ( element(esk2_2(X184,X185),powerset(X184))
| the_carrier(X185) != powerset(X184)
| X185 = boole_lattice(X184)
| ~ strict_latt_str(X185)
| ~ latt_str(X185) )
& ( apply_binary(the_L_join(X185),esk1_2(X184,X185),esk2_2(X184,X185)) != subset_union2(X184,esk1_2(X184,X185),esk2_2(X184,X185))
| apply_binary(the_L_meet(X185),esk1_2(X184,X185),esk2_2(X184,X185)) != subset_intersection2(X184,esk1_2(X184,X185),esk2_2(X184,X185))
| the_carrier(X185) != powerset(X184)
| X185 = boole_lattice(X184)
| ~ strict_latt_str(X185)
| ~ latt_str(X185) ) ),
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_30,plain,
! [X201] :
( strict_latt_str(boole_lattice(X201))
& latt_str(boole_lattice(X201)) ),
inference(variable_rename,[status(thm)],[dt_k1_lattice3]) ).
fof(c_0_31,plain,
! [X1] :
( ~ empty_carrier(boole_lattice(X1))
& strict_latt_str(boole_lattice(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_lattice3]) ).
fof(c_0_32,negated_conjecture,
~ ! [X1,X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ! [X3] :
( element(X3,the_carrier(boole_lattice(X1)))
=> ( join(boole_lattice(X1),X2,X3) = set_union2(X2,X3)
& meet(boole_lattice(X1),X2,X3) = set_intersection2(X2,X3) ) ) ),
inference(assume_negation,[status(cth)],[t1_lattice3]) ).
fof(c_0_33,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_34,plain,
! [X227] :
( ( function(the_L_join(X227))
| ~ join_semilatt_str(X227) )
& ( quasi_total(the_L_join(X227),cartesian_product2(the_carrier(X227),the_carrier(X227)),the_carrier(X227))
| ~ join_semilatt_str(X227) )
& ( relation_of2_as_subset(the_L_join(X227),cartesian_product2(the_carrier(X227),the_carrier(X227)),the_carrier(X227))
| ~ join_semilatt_str(X227) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u2_lattices])])]) ).
fof(c_0_35,plain,
! [X221] :
( ~ join_semilatt_str(X221)
| one_sorted_str(X221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_lattices])]) ).
cnf(c_0_36,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_23]) ).
cnf(c_0_37,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_24]) ).
cnf(c_0_38,plain,
( function(the_L_meet(X1))
| ~ meet_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_39,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_20]) ).
cnf(c_0_40,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_25,c_0_26]) ).
cnf(c_0_41,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ meet_semilatt_str(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_42,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_29]) ).
cnf(c_0_43,plain,
strict_latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_44,plain,
latt_str(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,plain,
( the_carrier(X1) = powerset(X2)
| X1 != boole_lattice(X2)
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_46,plain,
! [X240] :
( ~ empty_carrier(boole_lattice(X240))
& strict_latt_str(boole_lattice(X240)) ),
inference(variable_rename,[status(thm)],[c_0_31]) ).
fof(c_0_47,negated_conjecture,
( element(esk19_0,the_carrier(boole_lattice(esk18_0)))
& element(esk20_0,the_carrier(boole_lattice(esk18_0)))
& ( join(boole_lattice(esk18_0),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| meet(boole_lattice(esk18_0),esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
fof(c_0_48,plain,
! [X190,X191,X192] :
( empty_carrier(X190)
| ~ join_semilatt_str(X190)
| ~ element(X191,the_carrier(X190))
| ~ element(X192,the_carrier(X190))
| join(X190,X191,X192) = apply_binary_as_element(the_carrier(X190),the_carrier(X190),the_carrier(X190),the_L_join(X190),X191,X192) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])]) ).
cnf(c_0_49,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_34]) ).
cnf(c_0_50,plain,
( one_sorted_str(X1)
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,plain,
( apply_binary(the_L_meet(X1),X2,X3) = meet(X1,X2,X3)
| empty_carrier(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_52,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_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_53,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_45]),c_0_43]),c_0_44])]) ).
cnf(c_0_54,plain,
~ empty_carrier(boole_lattice(X1)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,negated_conjecture,
element(esk20_0,the_carrier(boole_lattice(esk18_0))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_56,negated_conjecture,
element(esk19_0,the_carrier(boole_lattice(esk18_0))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,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_29]) ).
cnf(c_0_58,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_48]) ).
cnf(c_0_59,plain,
( function(the_L_join(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_60,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_34]) ).
cnf(c_0_61,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_25,c_0_49]) ).
cnf(c_0_62,plain,
( empty_carrier(X1)
| ~ empty(the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_50]) ).
cnf(c_0_63,negated_conjecture,
( join(boole_lattice(esk18_0),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| meet(boole_lattice(esk18_0),esk19_0,esk20_0) != set_intersection2(esk19_0,esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_64,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_53])]),c_0_54]) ).
cnf(c_0_65,negated_conjecture,
element(esk20_0,powerset(esk18_0)),
inference(rw,[status(thm)],[c_0_55,c_0_53]) ).
cnf(c_0_66,negated_conjecture,
element(esk19_0,powerset(esk18_0)),
inference(rw,[status(thm)],[c_0_56,c_0_53]) ).
cnf(c_0_67,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_57]),c_0_43]),c_0_44])]) ).
cnf(c_0_68,plain,
( apply_binary(the_L_join(X1),X2,X3) = join(X1,X2,X3)
| empty_carrier(X1)
| ~ join_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_36]),c_0_59]),c_0_60]),c_0_61]),c_0_62]) ).
cnf(c_0_69,negated_conjecture,
( join(boole_lattice(esk18_0),esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| set_intersection2(esk19_0,esk20_0) != subset_intersection2(esk18_0,esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_66])]) ).
cnf(c_0_70,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(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_53]),c_0_53])]),c_0_54]) ).
fof(c_0_71,plain,
! [X222] :
( ( meet_semilatt_str(X222)
| ~ latt_str(X222) )
& ( join_semilatt_str(X222)
| ~ latt_str(X222) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
cnf(c_0_72,negated_conjecture,
( subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| set_intersection2(esk19_0,esk20_0) != subset_intersection2(esk18_0,esk19_0,esk20_0)
| ~ meet_semilatt_str(boole_lattice(esk18_0))
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_65]),c_0_66])]) ).
cnf(c_0_73,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_74,negated_conjecture,
( subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| set_intersection2(esk19_0,esk20_0) != subset_intersection2(esk18_0,esk19_0,esk20_0)
| ~ join_semilatt_str(boole_lattice(esk18_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_44])]) ).
cnf(c_0_75,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_76,plain,
! [X289,X290,X291] :
( ~ element(X290,powerset(X289))
| ~ element(X291,powerset(X289))
| subset_intersection2(X289,X290,X291) = set_intersection2(X290,X291) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1])]) ).
cnf(c_0_77,negated_conjecture,
( subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| set_intersection2(esk19_0,esk20_0) != subset_intersection2(esk18_0,esk19_0,esk20_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_44])]) ).
cnf(c_0_78,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_76]) ).
cnf(c_0_79,negated_conjecture,
( subset_intersection2(X1,esk19_0,esk20_0) != subset_intersection2(esk18_0,esk19_0,esk20_0)
| subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0)
| ~ element(esk20_0,powerset(X1))
| ~ element(esk19_0,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
fof(c_0_80,plain,
! [X286,X287,X288] :
( ~ element(X287,powerset(X286))
| ~ element(X288,powerset(X286))
| subset_union2(X286,X287,X288) = set_union2(X287,X288) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])]) ).
cnf(c_0_81,negated_conjecture,
subset_union2(esk18_0,esk19_0,esk20_0) != set_union2(esk19_0,esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_79]),c_0_65]),c_0_66])]) ).
cnf(c_0_82,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_80]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_65]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU343+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:58:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 3.90/3.15 % Version : CSE_E---1.7
% 3.90/3.15 % Problem : theBenchmark.p
% 3.90/3.15 % SZS status Theorem for theBenchmark.p
% 3.90/3.15 % SZS output start CNFRefutation
% See solution above
% 3.90/3.16 % Total time : 2.374s
%------------------------------------------------------------------------------