%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU326+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 05:11:29 PM UTC 2026
% Result : Theorem 3.63s 3.04s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 11 unt; 0 def)
% Number of atoms : 81 ( 37 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 79 ( 28 ~; 16 |; 29 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(t10_tops_2,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
fof(t46_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_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/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
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/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(c_0_6,plain,
! [X3003] :
( ~ empty(X3003)
| X3003 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_7,plain,
! [X2187] :
( element(esk130_1(X2187),powerset(X2187))
& empty(esk130_1(X2187))
& relation(esk130_1(X2187))
& function(esk130_1(X2187))
& one_to_one(esk130_1(X2187))
& epsilon_transitive(esk130_1(X2187))
& epsilon_connected(esk130_1(X2187))
& ordinal(esk130_1(X2187))
& natural(esk130_1(X2187))
& finite(esk130_1(X2187)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(c_0_8,negated_conjecture,
~ ! [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 ) ) ),
inference(assume_negation,[status(cth)],[t10_tops_2]) ).
cnf(c_0_9,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
empty(esk130_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,lemma,
! [X2916,X2917] :
( ~ element(X2917,powerset(powerset(X2916)))
| X2917 = empty_set
| complements_of_subsets(X2916,X2917) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(c_0_12,negated_conjecture,
( element(esk313_0,powerset(powerset(esk312_0)))
& ( complements_of_subsets(esk312_0,esk313_0) != empty_set
| esk313_0 != empty_set )
& ( esk313_0 = empty_set
| esk313_0 != empty_set )
& ( complements_of_subsets(esk312_0,esk313_0) != empty_set
| complements_of_subsets(esk312_0,esk313_0) = empty_set )
& ( esk313_0 = empty_set
| complements_of_subsets(esk312_0,esk313_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_13,plain,
! [X2109,X2110] :
( ~ element(X2110,powerset(powerset(X2109)))
| complements_of_subsets(X2109,complements_of_subsets(X2109,X2110)) = X2110 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(c_0_14,plain,
element(esk130_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
esk130_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_16,plain,
! [X1979,X1980] :
( ~ element(X1980,powerset(powerset(X1979)))
| element(complements_of_subsets(X1979,X1980),powerset(powerset(X1979))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
cnf(c_0_17,lemma,
( X1 = empty_set
| ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk313_0 = empty_set
| complements_of_subsets(esk312_0,esk313_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
element(esk313_0,powerset(powerset(esk312_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( complements_of_subsets(esk312_0,esk313_0) != empty_set
| esk313_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
esk313_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_25,plain,
complements_of_subsets(X1,complements_of_subsets(X1,empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
element(complements_of_subsets(X1,empty_set),powerset(powerset(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
complements_of_subsets(esk312_0,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).
cnf(c_0_28,lemma,
complements_of_subsets(X1,empty_set) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_25]),c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU326+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n003.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 02:57:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.63/3.04 % Version : CSE_E---1.7
% 3.63/3.04 % Problem : theBenchmark.p
% 3.63/3.04 % SZS status Theorem for theBenchmark.p
% 3.63/3.04 % SZS output start CNFRefutation
% See solution above
% 3.63/3.05 % Total time : 2.534s
%------------------------------------------------------------------------------