%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:24:49 PM UTC 2026
% Result : Theorem 0.37s 0.48s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 50 ( 17 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 21 ~; 10 |; 6 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_tex_2,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
fof(d2_tex_2,axiom,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
fof(rc2_tex_2,axiom,
! [X1] :
? [X2] :
( ~ proper_element(X2,powerset(X1))
& element(X2,powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tex_2) ).
fof(t99_zfmisc_1,lemma,
! [X1] : union(powerset(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
inference(assume_negation,[status(cth)],[t5_tex_2]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
inference(fof_simplification,[status(thm)],[d2_tex_2]) ).
fof(c_0_7,plain,
! [X1] :
? [X2] :
( ~ proper_element(X2,powerset(X1))
& element(X2,powerset(X1)) ),
inference(fof_simplification,[status(thm)],[rc2_tex_2]) ).
fof(c_0_8,negated_conjecture,
( ( esk2_0 != esk1_0
| proper_element(esk2_0,powerset(esk1_0)) )
& ( esk2_0 = esk1_0
| ~ proper_element(esk2_0,powerset(esk1_0)) )
& element(esk2_0,powerset(esk1_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,plain,
! [X23,X24] :
( ( ~ element(X24,X23)
| proper_element(X24,X23)
| X24 = union(X23) )
& ( ~ element(X24,X23)
| X24 != union(X23)
| ~ proper_element(X24,X23) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,lemma,
! [X68] : union(powerset(X68)) = X68,
inference(variable_rename,[status(thm)],[t99_zfmisc_1]) ).
fof(c_0_11,plain,
! [X25] :
( ~ proper_element(esk3_1(X25),powerset(X25))
& element(esk3_1(X25),powerset(X25)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,negated_conjecture,
( ~ proper_element(esk2_0,powerset(esk1_0))
| esk2_0 = esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ element(X1,X2)
| proper_element(X1,X2)
| X1 = union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,lemma,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
~ proper_element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk2_0 != esk1_0
| proper_element(esk2_0,powerset(esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
esk1_0 = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]) ).
cnf(c_0_20,plain,
esk3_1(X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_14]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
proper_element(esk2_0,powerset(esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19])]) ).
cnf(c_0_22,plain,
~ proper_element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_21,c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 06:14:40 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.12/0.48 % Version: 3.5.1
% 0.12/0.48 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.12/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.48 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.12/0.48 % Starting new_bool_3 with 600s (2) cores
% 0.12/0.48 % Starting new_bool_1 with 600s (2) cores
% 0.12/0.48 % Starting sh5l with 300s (1) cores
% 0.12/0.48 % new_bool_3 with pid 1150198 completed with status 0
% 0.12/0.48 % Result found by new_bool_3
% 0.12/0.48 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.12/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.48 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.12/0.48 % Starting new_bool_3 with 600s (2) cores
% 0.12/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.12/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.12/0.48 % Search class: FGHSM-FSLM31-MFFFFFNN
% 0.12/0.48 % Scheduled 8 strats onto 2 cores with 600 seconds (600 total)
% 0.12/0.48 % Starting SubtermCWHack with 55s (1) cores
% 0.12/0.48 % Starting new_bool_3 with 61s (1) cores
% 0.12/0.48 % SubtermCWHack with pid 1150202 completed with status 0
% 0.37/0.48 % Result found by SubtermCWHack
% 0.37/0.48 % Preprocessing class: FSLMSMSSSSSNFFN.
% 0.37/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.48 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 0.37/0.48 % Starting new_bool_3 with 600s (2) cores
% 0.37/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.37/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/0.48 % Search class: FGHSM-FSLM31-MFFFFFNN
% 0.37/0.48 % Scheduled 8 strats onto 2 cores with 600 seconds (600 total)
% 0.37/0.48 % Starting SubtermCWHack with 55s (1) cores
% 0.37/0.48 % Preprocessing time : 0.004 s
% 0.37/0.48
% 0.37/0.48 % Proof found!
% 0.37/0.48 % SZS status Theorem
% 0.37/0.48 % SZS output start CNFRefutation
% See solution above
% 0.37/0.48 % Parsed axioms : 670
% 0.37/0.48 % Removed by relevancy pruning/SinE : 611
% 0.37/0.48 % Initial clauses : 360
% 0.37/0.48 % Removed in clause preprocessing : 2
% 0.37/0.48 % Initial clauses in saturation : 358
% 0.37/0.48 % Processed clauses : 271
% 0.37/0.48 % ...of these trivial : 3
% 0.37/0.48 % ...subsumed : 49
% 0.37/0.48 % ...remaining for further processing : 219
% 0.37/0.48 % Other redundant clauses eliminated : 6
% 0.37/0.48 % Clauses deleted for lack of memory : 0
% 0.37/0.48 % Backward-subsumed : 2
% 0.37/0.48 % Backward-rewritten : 16
% 0.37/0.48 % Generated clauses : 432
% 0.37/0.48 % ...of the previous two non-redundant : 395
% 0.37/0.48 % ...aggressively subsumed : 0
% 0.37/0.48 % Contextual simplify-reflections : 3
% 0.37/0.48 % Paramodulations : 425
% 0.37/0.48 % Factorizations : 0
% 0.37/0.48 % NegExts : 0
% 0.37/0.48 % Equation resolutions : 6
% 0.37/0.48 % Disequality decompositions : 0
% 0.37/0.48 % Total rewrite steps : 72
% 0.37/0.48 % ...of those cached : 47
% 0.37/0.48 % Propositional unsat checks : 0
% 0.37/0.48 % Propositional check models : 0
% 0.37/0.48 % Propositional check unsatisfiable : 0
% 0.37/0.48 % Propositional clauses : 0
% 0.37/0.48 % Propositional clauses after purity: 0
% 0.37/0.48 % Propositional unsat core size : 0
% 0.37/0.48 % Propositional preprocessing time : 0.000
% 0.37/0.48 % Propositional encoding time : 0.000
% 0.37/0.48 % Propositional solver time : 0.000
% 0.37/0.48 % Success case prop preproc time : 0.000
% 0.37/0.48 % Success case prop encoding time : 0.000
% 0.37/0.48 % Success case prop solver time : 0.000
% 0.37/0.48 % Current number of processed clauses : 194
% 0.37/0.48 % Positive orientable unit clauses : 32
% 0.37/0.48 % Positive unorientable unit clauses: 0
% 0.37/0.48 % Negative unit clauses : 5
% 0.37/0.48 % Non-unit-clauses : 157
% 0.37/0.48 % Current number of unprocessed clauses: 482
% 0.37/0.48 % ...number of literals in the above : 2142
% 0.37/0.48 % Current number of archived formulas : 0
% 0.37/0.48 % Current number of archived clauses : 19
% 0.37/0.48 % Clause-clause subsumption calls (NU) : 5762
% 0.37/0.48 % Rec. Clause-clause subsumption calls : 5237
% 0.37/0.48 % Non-unit clause-clause subsumptions : 52
% 0.37/0.48 % Unit Clause-clause subsumption calls : 311
% 0.37/0.48 % Rewrite failures with RHS unbound : 0
% 0.37/0.48 % BW rewrite match attempts : 3
% 0.37/0.48 % BW rewrite match successes : 3
% 0.37/0.48 % Condensation attempts : 0
% 0.37/0.48 % Condensation successes : 0
% 0.37/0.48 % Termbank termtop insertions : 36275
% 0.37/0.48 % Search garbage collected termcells : 9985
% 0.37/0.48
% 0.37/0.48 % -------------------------------------------------
% 0.37/0.48 % User time : 0.024 s
% 0.37/0.48 % System time : 0.010 s
% 0.37/0.48 % Total time : 0.034 s
% 0.37/0.48 % Maximum resident set size: 5324 pages
% 0.37/0.48
% 0.37/0.48 % -------------------------------------------------
% 0.37/0.48 % User time : 0.060 s
% 0.37/0.48 % System time : 0.016 s
% 0.37/0.48 % Total time : 0.076 s
% 0.37/0.48 % Maximum resident set size: 5376 pages
% 0.37/0.48 % E exiting
%------------------------------------------------------------------------------