%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU328+2 : 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 : n016.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 05:11:30 PM UTC 2026
% Result : Theorem 5.36s 4.36s
% Output : CNFRefutation 5.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 20 unt; 0 def)
% Number of atoms : 124 ( 52 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 106 ( 39 ~; 28 |; 24 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 4 sgn 44 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_tops_2,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_tops_2) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(dt_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(union_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(redefinition_k5_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> union_of_subsets(X1,X2) = union(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(dt_k6_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(meet_of_subsets(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_finset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(t11_tops_2,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> meet_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,union_of_subsets(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11_tops_2) ).
fof(t10_tops_2,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( X2 != empty_set
=> union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_complement(X1,meet_of_subsets(X1,X2)) ) ),
inference(assume_negation,[status(cth)],[t12_tops_2]) ).
fof(c_0_13,plain,
! [X1983,X1984] :
( ~ element(X1984,powerset(powerset(X1983)))
| element(complements_of_subsets(X1983,X1984),powerset(powerset(X1983))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(c_0_14,negated_conjecture,
( element(esk313_0,powerset(powerset(esk312_0)))
& esk313_0 != empty_set
& union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,meet_of_subsets(esk312_0,esk313_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X1968,X1969] :
( ~ element(X1969,powerset(powerset(X1968)))
| element(union_of_subsets(X1968,X1969),powerset(X1968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).
cnf(c_0_16,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
element(esk313_0,powerset(powerset(esk312_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X2233,X2234] :
( ~ element(X2234,powerset(powerset(X2233)))
| union_of_subsets(X2233,X2234) = union(X2234) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1])]) ).
fof(c_0_19,plain,
! [X1976,X1977] :
( ~ element(X1977,powerset(powerset(X1976)))
| element(meet_of_subsets(X1976,X1977),powerset(X1976)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_setfam_1])]) ).
fof(c_0_20,plain,
! [X2110,X2111] :
( ~ element(X2111,powerset(X2110))
| subset_complement(X2110,subset_complement(X2110,X2111)) = X2111 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
cnf(c_0_21,plain,
( element(union_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
element(complements_of_subsets(esk312_0,esk313_0),powerset(powerset(esk312_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X2113,X2114] :
( ~ element(X2114,powerset(powerset(X2113)))
| complements_of_subsets(X2113,complements_of_subsets(X2113,X2114)) = X2114 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(c_0_24,plain,
( union_of_subsets(X2,X1) = union(X1)
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X1849,X1850] :
( ~ element(X1850,powerset(X1849))
| subset_complement(X1849,X1850) = set_difference(X1849,X1850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
cnf(c_0_26,plain,
( element(meet_of_subsets(X2,X1),powerset(X2))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X3011] :
( ~ empty(X3011)
| X3011 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_28,plain,
! [X2191] :
( element(esk130_1(X2191),powerset(X2191))
& empty(esk130_1(X2191))
& relation(esk130_1(X2191))
& function(esk130_1(X2191))
& one_to_one(esk130_1(X2191))
& epsilon_transitive(esk130_1(X2191))
& epsilon_connected(esk130_1(X2191))
& ordinal(esk130_1(X2191))
& natural(esk130_1(X2191))
& finite(esk130_1(X2191)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
cnf(c_0_29,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
element(union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)),powerset(esk312_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_31,lemma,
! [X2649,X2650] :
( ~ element(X2650,powerset(powerset(X2649)))
| X2650 = empty_set
| meet_of_subsets(X2649,complements_of_subsets(X2649,X2650)) = subset_complement(X2649,union_of_subsets(X2649,X2650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t11_tops_2])]) ).
cnf(c_0_32,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,negated_conjecture,
union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,meet_of_subsets(esk312_0,esk313_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) = union(complements_of_subsets(esk312_0,esk313_0)),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_35,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,negated_conjecture,
element(meet_of_subsets(esk312_0,esk313_0),powerset(esk312_0)),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
fof(c_0_37,lemma,
! [X2625,X2626] :
( ( X2626 = empty_set
| complements_of_subsets(X2625,X2626) != empty_set
| ~ element(X2626,powerset(powerset(X2625))) )
& ( complements_of_subsets(X2625,X2626) = empty_set
| X2626 != empty_set
| ~ element(X2626,powerset(powerset(X2625))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_tops_2])])]) ).
cnf(c_0_38,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
empty(esk130_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
subset_complement(esk312_0,subset_complement(esk312_0,union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)))) = union_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_41,lemma,
( X1 = empty_set
| meet_of_subsets(X2,complements_of_subsets(X2,X1)) = subset_complement(X2,union_of_subsets(X2,X1))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,negated_conjecture,
complements_of_subsets(esk312_0,complements_of_subsets(esk312_0,esk313_0)) = esk313_0,
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_43,negated_conjecture,
union(complements_of_subsets(esk312_0,esk313_0)) != subset_complement(esk312_0,meet_of_subsets(esk312_0,esk313_0)),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_44,negated_conjecture,
subset_complement(esk312_0,meet_of_subsets(esk312_0,esk313_0)) = set_difference(esk312_0,meet_of_subsets(esk312_0,esk313_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,lemma,
( complements_of_subsets(X1,X2) = empty_set
| X2 != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
element(esk130_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_47,plain,
esk130_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
subset_complement(esk312_0,subset_complement(esk312_0,union(complements_of_subsets(esk312_0,esk313_0)))) = union(complements_of_subsets(esk312_0,esk313_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_34]),c_0_34]) ).
cnf(c_0_49,negated_conjecture,
( subset_complement(esk312_0,union(complements_of_subsets(esk312_0,esk313_0))) = meet_of_subsets(esk312_0,esk313_0)
| complements_of_subsets(esk312_0,esk313_0) = empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_22]),c_0_42]),c_0_34]) ).
cnf(c_0_50,negated_conjecture,
union(complements_of_subsets(esk312_0,esk313_0)) != set_difference(esk312_0,meet_of_subsets(esk312_0,esk313_0)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,lemma,
( complements_of_subsets(X1,empty_set) = empty_set
| ~ element(empty_set,powerset(powerset(X1))) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_52,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
complements_of_subsets(esk312_0,esk313_0) = empty_set,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_44]),c_0_50]) ).
cnf(c_0_54,lemma,
complements_of_subsets(X1,empty_set) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_55,negated_conjecture,
esk313_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_53]),c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU328+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:57:51 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 5.36/4.36 % Version : CSE_E---1.7
% 5.36/4.36 % Problem : theBenchmark.p
% 5.36/4.36 % SZS status Theorem for theBenchmark.p
% 5.36/4.36 % SZS output start CNFRefutation
% See solution above
% 5.36/4.36 % Total time : 3.537s
%------------------------------------------------------------------------------