%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU326+1 : 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 : n007.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 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 73 ( 43 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 78 ( 36 ~; 17 |; 17 &)
% ( 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 : 38 ( 4 sgn 24 !; 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] :
( empty(X2)
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t46_setfam_1,axiom,
! [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(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(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,
! [X8] :
( X8 = empty_set
| ~ empty(X8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
fof(c_0_8,plain,
! [X22] :
( empty(esk5_1(X22))
& element(esk5_1(X22),powerset(X22)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_9,plain,
! [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_6]) ).
cnf(c_0_11,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
empty(esk5_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X6,X7] :
( complements_of_subsets(X6,X7) != empty_set
| X7 = empty_set
| ~ element(X7,powerset(powerset(X6))) ),
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])])])])]) ).
fof(c_0_15,plain,
! [X11,X12] :
( complements_of_subsets(X11,complements_of_subsets(X11,X12)) = X12
| ~ element(X12,powerset(powerset(X11))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])])]) ).
cnf(c_0_16,plain,
element(esk5_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
esk5_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( 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_19,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_20,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_23,plain,
! [X9,X10] :
( element(complements_of_subsets(X9,X10),powerset(powerset(X9)))
| ~ element(X10,powerset(powerset(X9))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])])]) ).
cnf(c_0_24,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_25,negated_conjecture,
esk2_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_26,plain,
( ~ element(complements_of_subsets(X1,empty_set),powerset(powerset(X1)))
| 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_18,c_0_21])]),c_0_22])]) ).
cnf(c_0_27,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,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_24,c_0_25]),c_0_25])]) ).
cnf(c_0_29,plain,
complements_of_subsets(X1,empty_set) = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22])]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 06:09:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.43 % Version: 3.5.1
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.43 % Starting sh5l with 300s (1) cores
% 0.13/0.43 % new_bool_3 with pid 349490 completed with status 0
% 0.13/0.43 % Result found by new_bool_3
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.43 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.13/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.43 % SubtermCWHack with pid 349495 completed with status 0
% 0.13/0.43 % Result found by SubtermCWHack
% 0.13/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.43 % Search class: FGHSS-FFMM21-SFFFFFNN
% 0.13/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.43 % Preprocessing time : 0.001 s
% 0.13/0.43
% 0.13/0.43 % Proof found!
% 0.13/0.43 % SZS status Theorem
% 0.13/0.43 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43 % Parsed axioms : 38
% 0.13/0.43 % Removed by relevancy pruning/SinE : 16
% 0.13/0.43 % Initial clauses : 52
% 0.13/0.43 % Removed in clause preprocessing : 2
% 0.13/0.43 % Initial clauses in saturation : 50
% 0.13/0.43 % Processed clauses : 129
% 0.13/0.43 % ...of these trivial : 0
% 0.13/0.43 % ...subsumed : 29
% 0.13/0.43 % ...remaining for further processing : 100
% 0.13/0.43 % Other redundant clauses eliminated : 1
% 0.13/0.43 % Clauses deleted for lack of memory : 0
% 0.13/0.43 % Backward-subsumed : 0
% 0.13/0.43 % Backward-rewritten : 21
% 0.13/0.43 % Generated clauses : 119
% 0.13/0.43 % ...of the previous two non-redundant : 94
% 0.13/0.43 % ...aggressively subsumed : 0
% 0.13/0.43 % Contextual simplify-reflections : 0
% 0.13/0.43 % Paramodulations : 118
% 0.13/0.43 % Factorizations : 0
% 0.13/0.43 % NegExts : 0
% 0.13/0.43 % Equation resolutions : 1
% 0.13/0.43 % Disequality decompositions : 0
% 0.13/0.43 % Total rewrite steps : 67
% 0.13/0.43 % ...of those cached : 51
% 0.13/0.43 % Propositional unsat checks : 0
% 0.13/0.43 % Propositional check models : 0
% 0.13/0.43 % Propositional check unsatisfiable : 0
% 0.13/0.43 % Propositional clauses : 0
% 0.13/0.43 % Propositional clauses after purity: 0
% 0.13/0.43 % Propositional unsat core size : 0
% 0.13/0.43 % Propositional preprocessing time : 0.000
% 0.13/0.43 % Propositional encoding time : 0.000
% 0.13/0.43 % Propositional solver time : 0.000
% 0.13/0.43 % Success case prop preproc time : 0.000
% 0.13/0.43 % Success case prop encoding time : 0.000
% 0.13/0.43 % Success case prop solver time : 0.000
% 0.13/0.43 % Current number of processed clauses : 79
% 0.13/0.43 % Positive orientable unit clauses : 16
% 0.13/0.43 % Positive unorientable unit clauses: 0
% 0.13/0.43 % Negative unit clauses : 2
% 0.13/0.43 % Non-unit-clauses : 61
% 0.13/0.43 % Current number of unprocessed clauses: 15
% 0.13/0.43 % ...number of literals in the above : 45
% 0.13/0.43 % Current number of archived formulas : 0
% 0.13/0.43 % Current number of archived clauses : 21
% 0.13/0.43 % Clause-clause subsumption calls (NU) : 394
% 0.13/0.43 % Rec. Clause-clause subsumption calls : 394
% 0.13/0.43 % Non-unit clause-clause subsumptions : 17
% 0.13/0.43 % Unit Clause-clause subsumption calls : 0
% 0.13/0.43 % Rewrite failures with RHS unbound : 0
% 0.13/0.43 % BW rewrite match attempts : 4
% 0.13/0.43 % BW rewrite match successes : 4
% 0.13/0.43 % Condensation attempts : 0
% 0.13/0.43 % Condensation successes : 0
% 0.13/0.43 % Termbank termtop insertions : 4027
% 0.13/0.43 % Search garbage collected termcells : 499
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.009 s
% 0.13/0.43 % System time : 0.000 s
% 0.13/0.43 % Total time : 0.009 s
% 0.13/0.43 % Maximum resident set size: 3664 pages
% 0.13/0.43
% 0.13/0.43 % -------------------------------------------------
% 0.13/0.43 % User time : 0.011 s
% 0.13/0.43 % System time : 0.004 s
% 0.13/0.43 % Total time : 0.015 s
% 0.13/0.43 % Maximum resident set size: 4864 pages
% 0.13/0.43 % E exiting
%------------------------------------------------------------------------------