%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU326+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:43 PM UTC 2026
% Result : Theorem 0.65s 0.80s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 88 ( 47 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 93 ( 44 ~; 20 |; 21 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 47 ( 4 sgn 30 !; 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(t46_setfam_1,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( complements_of_subsets(X1,X2) = empty_set
& 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] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
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(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(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
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]) ).
fof(c_0_9,lemma,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( complements_of_subsets(X1,X2) = empty_set
& X2 != empty_set ) ),
inference(fof_simplification,[status(thm)],[t46_setfam_1]) ).
fof(c_0_10,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(fof_simplification,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X34] :
( X34 = empty_set
| ~ empty(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_12,plain,
! [X71] :
( empty(esk11_1(X71))
& element(esk11_1(X71),powerset(X71)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_13,lemma,
! [X44,X45] :
( complements_of_subsets(X44,X45) != empty_set
| X45 = empty_set
| ~ element(X45,powerset(powerset(X44))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,negated_conjecture,
( ( complements_of_subsets(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set )
& ( complements_of_subsets(esk1_0,esk2_0) = empty_set
| complements_of_subsets(esk1_0,esk2_0) != empty_set )
& ( esk2_0 != empty_set
| esk2_0 = empty_set )
& ( esk2_0 != empty_set
| complements_of_subsets(esk1_0,esk2_0) != empty_set )
& element(esk2_0,powerset(powerset(esk1_0))) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])]) ).
cnf(c_0_15,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
empty(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,lemma,
( complements_of_subsets(X2,X1) != empty_set
| ~ element(X1,powerset(powerset(X2)))
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = empty_set
| esk2_0 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X1,X2] :
~ ( empty(X2)
& X1 != X2
& empty(X1) ),
inference(fof_simplification,[status(thm)],[t8_boole]) ).
fof(c_0_21,plain,
! [X42,X43] :
( complements_of_subsets(X42,complements_of_subsets(X42,X43)) = X43
| ~ element(X43,powerset(powerset(X42))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])])]) ).
cnf(c_0_22,plain,
element(esk11_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
esk11_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_24,plain,
! [X40,X41] :
( element(complements_of_subsets(X40,X41),powerset(powerset(X40)))
| ~ element(X41,powerset(powerset(X40))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])])]) ).
cnf(c_0_25,negated_conjecture,
( esk2_0 != empty_set
| complements_of_subsets(esk1_0,esk2_0) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
esk2_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
fof(c_0_27,plain,
! [X141,X142] :
( ~ empty(X142)
| X141 = X142
| ~ empty(X141) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_28,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
complements_of_subsets(esk1_0,empty_set) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26])]) ).
cnf(c_0_32,plain,
( ~ empty(X2)
| ~ empty(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_34,plain,
complements_of_subsets(X1,complements_of_subsets(X1,empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
element(complements_of_subsets(X1,empty_set),powerset(powerset(X1))),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
~ empty(complements_of_subsets(esk1_0,empty_set)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32])]),c_0_33])]) ).
cnf(c_0_37,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_34]),c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU326+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 06:17:28 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.51 Running first-order theorem proving
% 0.28/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.65/0.80 % Version: 3.5.1
% 0.65/0.80 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.65/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.80 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.65/0.80 % Starting new_bool_3 with 600s (2) cores
% 0.65/0.80 % Starting new_bool_1 with 600s (2) cores
% 0.65/0.80 % Starting sh5l with 300s (1) cores
% 0.65/0.80 % new_bool_1 with pid 2369464 completed with status 0
% 0.65/0.80 % Result found by new_bool_1
% 0.65/0.80 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.65/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.80 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.65/0.80 % Starting new_bool_3 with 600s (2) cores
% 0.65/0.80 % Starting new_bool_1 with 600s (2) cores
% 0.65/0.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.65/0.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.65/0.80 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.65/0.80 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 0.65/0.80 % Starting SubtermCWHack with 55s (1) cores
% 0.65/0.80 % Starting new_bool_1 with 61s (1) cores
% 0.65/0.80 % new_bool_1 with pid 2369467 completed with status 0
% 0.65/0.80 % Result found by new_bool_1
% 0.65/0.80 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.65/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.80 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.65/0.80 % Starting new_bool_3 with 600s (2) cores
% 0.65/0.80 % Starting new_bool_1 with 600s (2) cores
% 0.65/0.80 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.65/0.80 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.65/0.80 % Search class: FGHSM-FSLM32-MFFFFFNN
% 0.65/0.80 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 0.65/0.80 % Starting SubtermCWHack with 55s (1) cores
% 0.65/0.80 % Starting new_bool_1 with 61s (1) cores
% 0.65/0.80 % Preprocessing time : 0.011 s
% 0.65/0.80 % Presaturation interreduction done
% 0.65/0.80
% 0.65/0.80 % Proof found!
% 0.65/0.80 % SZS status Theorem
% 0.65/0.80 % SZS output start CNFRefutation
% See solution above
% 0.65/0.80 % Parsed axioms : 539
% 0.65/0.80 % Removed by relevancy pruning/SinE : 419
% 0.65/0.80 % Initial clauses : 657
% 0.65/0.80 % Removed in clause preprocessing : 4
% 0.65/0.80 % Initial clauses in saturation : 653
% 0.65/0.80 % Processed clauses : 1146
% 0.65/0.80 % ...of these trivial : 3
% 0.65/0.80 % ...subsumed : 156
% 0.65/0.80 % ...remaining for further processing : 987
% 0.65/0.80 % Other redundant clauses eliminated : 259
% 0.65/0.80 % Clauses deleted for lack of memory : 0
% 0.65/0.80 % Backward-subsumed : 8
% 0.65/0.80 % Backward-rewritten : 22
% 0.65/0.80 % Generated clauses : 858
% 0.65/0.80 % ...of the previous two non-redundant : 709
% 0.65/0.80 % ...aggressively subsumed : 0
% 0.65/0.80 % Contextual simplify-reflections : 126
% 0.65/0.80 % Paramodulations : 617
% 0.65/0.80 % Factorizations : 0
% 0.65/0.80 % NegExts : 0
% 0.65/0.80 % Equation resolutions : 260
% 0.65/0.80 % Disequality decompositions : 0
% 0.65/0.80 % Total rewrite steps : 201
% 0.65/0.80 % ...of those cached : 151
% 0.65/0.80 % Propositional unsat checks : 0
% 0.65/0.80 % Propositional check models : 0
% 0.65/0.80 % Propositional check unsatisfiable : 0
% 0.65/0.80 % Propositional clauses : 0
% 0.65/0.80 % Propositional clauses after purity: 0
% 0.65/0.80 % Propositional unsat core size : 0
% 0.65/0.80 % Propositional preprocessing time : 0.000
% 0.65/0.80 % Propositional encoding time : 0.000
% 0.65/0.80 % Propositional solver time : 0.000
% 0.65/0.80 % Success case prop preproc time : 0.000
% 0.65/0.80 % Success case prop encoding time : 0.000
% 0.65/0.80 % Success case prop solver time : 0.000
% 0.65/0.80 % Current number of processed clauses : 157
% 0.65/0.80 % Positive orientable unit clauses : 41
% 0.65/0.80 % Positive unorientable unit clauses: 0
% 0.65/0.80 % Negative unit clauses : 14
% 0.65/0.80 % Non-unit-clauses : 102
% 0.65/0.80 % Current number of unprocessed clauses: 815
% 0.65/0.80 % ...number of literals in the above : 3658
% 0.65/0.80 % Current number of archived formulas : 0
% 0.65/0.80 % Current number of archived clauses : 635
% 0.65/0.80 % Clause-clause subsumption calls (NU) : 270939
% 0.65/0.80 % Rec. Clause-clause subsumption calls : 14902
% 0.65/0.80 % Non-unit clause-clause subsumptions : 227
% 0.65/0.80 % Unit Clause-clause subsumption calls : 241
% 0.65/0.80 % Rewrite failures with RHS unbound : 0
% 0.65/0.80 % BW rewrite match attempts : 25
% 0.65/0.80 % BW rewrite match successes : 8
% 0.65/0.80 % Condensation attempts : 0
% 0.65/0.80 % Condensation successes : 0
% 0.65/0.80 % Termbank termtop insertions : 66162
% 0.65/0.80 % Search garbage collected termcells : 11202
% 0.65/0.80
% 0.65/0.80 % -------------------------------------------------
% 0.65/0.80 % User time : 0.213 s
% 0.65/0.80 % System time : 0.014 s
% 0.65/0.80 % Total time : 0.227 s
% 0.65/0.80 % Maximum resident set size: 5624 pages
% 0.65/0.80
% 0.65/0.80 % -------------------------------------------------
% 0.65/0.80 % User time : 0.409 s
% 0.65/0.80 % System time : 0.036 s
% 0.65/0.80 % Total time : 0.445 s
% 0.65/0.80 % Maximum resident set size: 5376 pages
% 0.65/0.80 % E exiting
%------------------------------------------------------------------------------