%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU326+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 : n013.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 1.34s 1.73s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 66 ( 38 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 67 ( 30 ~; 18 |; 13 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 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(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/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t46_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_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/sandbox2/benchmark/theBenchmark.p',dt_k7_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/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(c_0_6,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]) ).
fof(c_0_7,plain,
! [X122] :
( ~ empty(X122)
| X122 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_8,plain,
! [X103] :
( element(esk4_1(X103),powerset(X103))
& empty(esk4_1(X103)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_9,plain,
! [X114,X115] :
( ~ element(X115,powerset(powerset(X114)))
| X115 = empty_set
| complements_of_subsets(X114,X115) != empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).
fof(c_0_10,negated_conjecture,
( element(esk6_0,powerset(powerset(esk5_0)))
& ( complements_of_subsets(esk5_0,esk6_0) != empty_set
| esk6_0 != empty_set )
& ( esk6_0 = empty_set
| esk6_0 != empty_set )
& ( complements_of_subsets(esk5_0,esk6_0) != empty_set
| complements_of_subsets(esk5_0,esk6_0) = empty_set )
& ( esk6_0 = empty_set
| complements_of_subsets(esk5_0,esk6_0) = empty_set ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X93,X94] :
( ~ element(X94,powerset(powerset(X93)))
| element(complements_of_subsets(X93,X94),powerset(powerset(X93))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
empty(esk4_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,X1) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
element(esk6_0,powerset(powerset(esk5_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( esk6_0 = empty_set
| complements_of_subsets(esk5_0,esk6_0) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X98,X99] :
( ~ element(X99,powerset(powerset(X98)))
| complements_of_subsets(X98,complements_of_subsets(X98,X99)) = X99 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
cnf(c_0_19,plain,
element(esk4_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
esk4_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( complements_of_subsets(esk5_0,esk6_0) != empty_set
| esk6_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
esk6_0 = empty_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_23,plain,
( complements_of_subsets(X1,X2) = empty_set
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_24,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
complements_of_subsets(esk5_0,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22])]) ).
cnf(c_0_27,plain,
complements_of_subsets(X1,empty_set) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24])]),c_0_25])]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU326+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 : n013.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
% 1.34/1.73 % Version : CSE_E---1.7
% 1.34/1.73 % Problem : theBenchmark.p
% 1.34/1.73 % SZS status Theorem for theBenchmark.p
% 1.34/1.73 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------