%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU174+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 : n005.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 05:10:57 PM UTC 2026
% Result : Theorem 1.44s 1.80s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 104 ( 29 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 117 ( 50 ~; 42 |; 12 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 6 sgn 37 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t46_setfam_1,conjecture,
! [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(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(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d8_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
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_8,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
inference(assume_negation,[status(cth)],[t46_setfam_1]) ).
fof(c_0_9,plain,
! [X562] :
( ~ empty(X562)
| X562 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,plain,
! [X440] :
( element(esk22_1(X440),powerset(X440))
& empty(esk22_1(X440)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_11,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_12,plain,
! [X382,X383,X384,X385] :
( ( ~ in(X385,X384)
| in(subset_complement(X382,X385),X383)
| ~ element(X385,powerset(X382))
| X384 != complements_of_subsets(X382,X383)
| ~ element(X384,powerset(powerset(X382)))
| ~ element(X383,powerset(powerset(X382))) )
& ( ~ in(subset_complement(X382,X385),X383)
| in(X385,X384)
| ~ element(X385,powerset(X382))
| X384 != complements_of_subsets(X382,X383)
| ~ element(X384,powerset(powerset(X382)))
| ~ element(X383,powerset(powerset(X382))) )
& ( element(esk17_3(X382,X383,X384),powerset(X382))
| X384 = complements_of_subsets(X382,X383)
| ~ element(X384,powerset(powerset(X382)))
| ~ element(X383,powerset(powerset(X382))) )
& ( ~ in(esk17_3(X382,X383,X384),X384)
| ~ in(subset_complement(X382,esk17_3(X382,X383,X384)),X383)
| X384 = complements_of_subsets(X382,X383)
| ~ element(X384,powerset(powerset(X382)))
| ~ element(X383,powerset(powerset(X382))) )
& ( in(esk17_3(X382,X383,X384),X384)
| in(subset_complement(X382,esk17_3(X382,X383,X384)),X383)
| X384 = complements_of_subsets(X382,X383)
| ~ element(X384,powerset(powerset(X382)))
| ~ element(X383,powerset(powerset(X382))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_setfam_1])])])])]) ).
fof(c_0_13,plain,
! [X536,X537,X538] :
( ~ in(X536,X537)
| ~ element(X537,powerset(X538))
| element(X536,X538) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_14,plain,
! [X391,X392] :
( ~ element(X392,powerset(powerset(X391)))
| element(complements_of_subsets(X391,X392),powerset(powerset(X391))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).
fof(c_0_15,plain,
! [X406,X407] :
( ~ element(X407,powerset(powerset(X406)))
| complements_of_subsets(X406,complements_of_subsets(X406,X407)) = X407 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).
fof(c_0_16,negated_conjecture,
( element(esk28_0,powerset(powerset(esk27_0)))
& esk28_0 != empty_set
& complements_of_subsets(esk27_0,esk28_0) = empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_17,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
empty(esk22_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_19,plain,
! [X293,X294,X295] :
( ( X293 != empty_set
| ~ in(X294,X293) )
& ( in(esk2_1(X295),X295)
| X295 = empty_set ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
cnf(c_0_20,plain,
( in(subset_complement(X3,X1),X4)
| ~ in(X1,X2)
| ~ element(X1,powerset(X3))
| X2 != complements_of_subsets(X3,X4)
| ~ element(X2,powerset(powerset(X3)))
| ~ element(X4,powerset(powerset(X3))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
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_14]) ).
cnf(c_0_23,plain,
( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
| ~ element(X1,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
complements_of_subsets(esk27_0,esk28_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
element(esk28_0,powerset(powerset(esk27_0))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
element(esk22_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,plain,
esk22_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_28,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( in(subset_complement(X1,X2),X3)
| ~ element(X3,powerset(powerset(X1)))
| ~ in(X2,complements_of_subsets(X1,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_20,c_0_21])]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
complements_of_subsets(esk27_0,empty_set) = esk28_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
~ in(X1,esk28_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_34,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,negated_conjecture,
esk28_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU174+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
% 0.16/0.32 % Computer : n005.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:46:30 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.44/1.80 % Version : CSE_E---1.7
% 1.44/1.80 % Problem : theBenchmark.p
% 1.44/1.80 % SZS status Theorem for theBenchmark.p
% 1.44/1.80 % SZS output start CNFRefutation
% See solution above
% 1.54/1.80 % Total time : 1.373s
%------------------------------------------------------------------------------