%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU764^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 : Wed Sep 30 08:25:32 AM UTC 2026
% Result : Theorem 0.26s 0.42s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 15 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 472 ( 21 ~; 13 |; 7 &; 395 @)
% ( 3 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
binunion: $i > $i > $i ).
thf(decl_26,type,
binintersect: $i > $i > $i ).
thf(decl_27,type,
setminus: $i > $i > $i ).
thf(decl_28,type,
binunionT_lem: $o ).
thf(decl_29,type,
demorgan1: $o ).
thf(decl_30,type,
demorgan2: $o ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(decl_35,type,
esk5_0: $i ).
thf(woz1_2,conjecture,
( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X2 @ X3 ) @ ( binunion @ X4 @ X5 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X4 ) @ ( setminus @ X1 @ X5 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Yqvgu9zz4x/E---3.1_3435724.p',woz1_2) ).
thf(binunionT_lem,axiom,
( binunionT_lem
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binunion @ X2 @ X3 ) @ ( powerset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Yqvgu9zz4x/E---3.1_3435724.p',binunionT_lem) ).
thf(demorgan1,axiom,
( demorgan1
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binintersect @ X2 @ X3 ) )
= ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Yqvgu9zz4x/E---3.1_3435724.p',demorgan1) ).
thf(demorgan2,axiom,
( demorgan2
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binunion @ X2 @ X3 ) )
= ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Yqvgu9zz4x/E---3.1_3435724.p',demorgan2) ).
thf(c_0_4,negated_conjecture,
~ ( binunionT_lem
=> ( demorgan1
=> ( demorgan2
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X2 @ X3 ) @ ( binunion @ X4 @ X5 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X4 ) @ ( setminus @ X1 @ X5 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[woz1_2]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X20: $i,X21: $i] :
( ( in @ X21 @ ( powerset @ X20 ) )
=> ! [X22: $i] :
( ( in @ X22 @ ( powerset @ X20 ) )
=> ( in @ ( binunion @ X21 @ X22 ) @ ( powerset @ X20 ) ) ) )
=> ( ! [X23: $i,X24: $i] :
( ( in @ X24 @ ( powerset @ X23 ) )
=> ! [X25: $i] :
( ( in @ X25 @ ( powerset @ X23 ) )
=> ( ( setminus @ X23 @ ( binintersect @ X24 @ X25 ) )
= ( binunion @ ( setminus @ X23 @ X24 ) @ ( setminus @ X23 @ X25 ) ) ) ) )
=> ( ! [X26: $i,X27: $i] :
( ( in @ X27 @ ( powerset @ X26 ) )
=> ! [X28: $i] :
( ( in @ X28 @ ( powerset @ X26 ) )
=> ( ( setminus @ X26 @ ( binunion @ X27 @ X28 ) )
= ( binintersect @ ( setminus @ X26 @ X27 ) @ ( setminus @ X26 @ X28 ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ( setminus @ X1 @ ( binintersect @ ( binunion @ X2 @ X3 ) @ ( binunion @ X4 @ X5 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X3 ) ) @ ( binintersect @ ( setminus @ X1 @ X4 ) @ ( setminus @ X1 @ X5 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,binunionT_lem]),demorgan1]),demorgan2]) ).
thf(c_0_6,negated_conjecture,
! [X29: $i,X30: $i,X31: $i,X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ~ ( in @ X30 @ ( powerset @ X29 ) )
| ~ ( in @ X31 @ ( powerset @ X29 ) )
| ( in @ ( binunion @ X30 @ X31 ) @ ( powerset @ X29 ) ) )
& ( ~ ( in @ X33 @ ( powerset @ X32 ) )
| ~ ( in @ X34 @ ( powerset @ X32 ) )
| ( ( setminus @ X32 @ ( binintersect @ X33 @ X34 ) )
= ( binunion @ ( setminus @ X32 @ X33 ) @ ( setminus @ X32 @ X34 ) ) ) )
& ( ~ ( in @ X36 @ ( powerset @ X35 ) )
| ~ ( in @ X37 @ ( powerset @ X35 ) )
| ( ( setminus @ X35 @ ( binunion @ X36 @ X37 ) )
= ( binintersect @ ( setminus @ X35 @ X36 ) @ ( setminus @ X35 @ X37 ) ) ) )
& ( in @ esk2_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk3_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk5_0 @ ( powerset @ esk1_0 ) )
& ( ( setminus @ esk1_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk3_0 ) @ ( binunion @ esk4_0 @ esk5_0 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ esk1_0 @ esk2_0 ) @ ( setminus @ esk1_0 @ esk3_0 ) ) @ ( binintersect @ ( setminus @ esk1_0 @ esk4_0 ) @ ( setminus @ esk1_0 @ esk5_0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
thf(c_0_7,negated_conjecture,
( ( setminus @ esk1_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk3_0 ) @ ( binunion @ esk4_0 @ esk5_0 ) ) )
!= ( binunion @ ( binintersect @ ( setminus @ esk1_0 @ esk2_0 ) @ ( setminus @ esk1_0 @ esk3_0 ) ) @ ( binintersect @ ( setminus @ esk1_0 @ esk4_0 ) @ ( setminus @ esk1_0 @ esk5_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( setminus @ X2 @ ( binunion @ X1 @ X3 ) )
= ( binintersect @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
in @ esk5_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
( ( binunion @ ( binintersect @ ( setminus @ esk1_0 @ esk2_0 ) @ ( setminus @ esk1_0 @ esk3_0 ) ) @ ( setminus @ esk1_0 @ ( binunion @ esk4_0 @ esk5_0 ) ) )
!= ( setminus @ esk1_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk3_0 ) @ ( binunion @ esk4_0 @ esk5_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]) ).
thf(c_0_12,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
in @ esk2_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
( ( binunion @ ( setminus @ esk1_0 @ ( binunion @ esk2_0 @ esk3_0 ) ) @ ( setminus @ esk1_0 @ ( binunion @ esk4_0 @ esk5_0 ) ) )
!= ( setminus @ esk1_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk3_0 ) @ ( binunion @ esk4_0 @ esk5_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_12]),c_0_13])]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( setminus @ X2 @ ( binintersect @ X1 @ X3 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X3 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
( ~ ( in @ ( binunion @ esk4_0 @ esk5_0 ) @ ( powerset @ esk1_0 ) )
| ~ ( in @ ( binunion @ esk2_0 @ esk3_0 ) @ ( powerset @ esk1_0 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( binunion @ X1 @ X3 ) @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ ( binunion @ esk4_0 @ esk5_0 ) @ ( powerset @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_12]),c_0_13])]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU764^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n007.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.28 % CPULimit : 300
% 0.11/0.28 % WCLimit : 300
% 0.11/0.28 % DateTime : Tue Sep 29 14:21:25 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.34 Running higher-order theorem proving
% 0.26/0.36 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.Yqvgu9zz4x/E---3.1_3435724.p
% 0.26/0.42 % Version: 3.5.1-ho
% 0.26/0.42 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.26/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.42 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.26/0.42 % Starting post_as_ho8 with 300s (1) cores
% 0.26/0.42 % Starting post_as_ho3 with 300s (1) cores
% 0.26/0.42 % Starting post_as_ho2 with 300s (1) cores
% 0.26/0.42 % post_as_ho8 with pid 3435738 completed with status 0
% 0.26/0.42 % Result found by post_as_ho8
% 0.26/0.42 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.26/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.42 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.26/0.42 % Starting post_as_ho8 with 300s (1) cores
% 0.26/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.26/0.42 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.26/0.42 % Search class: HHUSF-FFSS21-MFFFMFNN
% 0.26/0.42 % partial match(2): HHUNF-FFSS21-SFFFMFNN
% 0.26/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.42 % SubtermCWHack with pid 3435742 completed with status 0
% 0.26/0.42 % Result found by SubtermCWHack
% 0.26/0.42 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.26/0.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.42 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.26/0.42 % Starting post_as_ho8 with 300s (1) cores
% 0.26/0.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.26/0.42 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.26/0.42 % Search class: HHUSF-FFSS21-MFFFMFNN
% 0.26/0.42 % partial match(2): HHUNF-FFSS21-SFFFMFNN
% 0.26/0.42 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.42 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.42 % Preprocessing time : 0.001 s
% 0.26/0.42
% 0.26/0.42 % Proof found!
% 0.26/0.42 % SZS status Theorem
% 0.26/0.42 % SZS output start CNFRefutation
% See solution above
% 0.26/0.42 % Parsed axioms : 12
% 0.26/0.42 % Removed by relevancy pruning/SinE : 8
% 0.26/0.42 % Initial clauses : 8
% 0.26/0.42 % Removed in clause preprocessing : 0
% 0.26/0.42 % Initial clauses in saturation : 8
% 0.26/0.42 % Processed clauses : 13
% 0.26/0.42 % ...of these trivial : 0
% 0.26/0.42 % ...subsumed : 0
% 0.26/0.42 % ...remaining for further processing : 13
% 0.26/0.42 % Other redundant clauses eliminated : 0
% 0.26/0.42 % Clauses deleted for lack of memory : 0
% 0.26/0.42 % Backward-subsumed : 1
% 0.26/0.42 % Backward-rewritten : 0
% 0.26/0.42 % Generated clauses : 8
% 0.26/0.42 % ...of the previous two non-redundant : 7
% 0.26/0.42 % ...aggressively subsumed : 0
% 0.26/0.42 % Contextual simplify-reflections : 0
% 0.26/0.42 % Paramodulations : 8
% 0.26/0.42 % Factorizations : 0
% 0.26/0.42 % NegExts : 0
% 0.26/0.42 % Equation resolutions : 0
% 0.26/0.42 % Disequality decompositions : 0
% 0.26/0.42 % Total rewrite steps : 10
% 0.26/0.42 % ...of those cached : 6
% 0.26/0.42 % Propositional unsat checks : 0
% 0.26/0.42 % Propositional check models : 0
% 0.26/0.42 % Propositional check unsatisfiable : 0
% 0.26/0.42 % Propositional clauses : 0
% 0.26/0.42 % Propositional clauses after purity: 0
% 0.26/0.42 % Propositional unsat core size : 0
% 0.26/0.42 % Propositional preprocessing time : 0.000
% 0.26/0.42 % Propositional encoding time : 0.000
% 0.26/0.42 % Propositional solver time : 0.000
% 0.26/0.42 % Success case prop preproc time : 0.000
% 0.26/0.42 % Success case prop encoding time : 0.000
% 0.26/0.42 % Success case prop solver time : 0.000
% 0.26/0.42 % Current number of processed clauses : 12
% 0.26/0.42 % Positive orientable unit clauses : 4
% 0.26/0.42 % Positive unorientable unit clauses: 0
% 0.26/0.42 % Negative unit clauses : 4
% 0.26/0.42 % Non-unit-clauses : 4
% 0.26/0.42 % Current number of unprocessed clauses: 2
% 0.26/0.42 % ...number of literals in the above : 8
% 0.26/0.42 % Current number of archived formulas : 0
% 0.26/0.42 % Current number of archived clauses : 1
% 0.26/0.42 % Clause-clause subsumption calls (NU) : 7
% 0.26/0.42 % Rec. Clause-clause subsumption calls : 2
% 0.26/0.42 % Non-unit clause-clause subsumptions : 0
% 0.26/0.42 % Unit Clause-clause subsumption calls : 1
% 0.26/0.42 % Rewrite failures with RHS unbound : 0
% 0.26/0.42 % BW rewrite match attempts : 0
% 0.26/0.42 % BW rewrite match successes : 0
% 0.26/0.42 % Condensation attempts : 0
% 0.26/0.42 % Condensation successes : 0
% 0.26/0.42 % Termbank termtop insertions : 1393
% 0.26/0.42 % Search garbage collected termcells : 374
% 0.26/0.42
% 0.26/0.42 % -------------------------------------------------
% 0.26/0.42 % User time : 0.006 s
% 0.26/0.42 % System time : 0.002 s
% 0.26/0.42 % Total time : 0.008 s
% 0.26/0.42 % Maximum resident set size: 3892 pages
% 0.26/0.42
% 0.26/0.42 % -------------------------------------------------
% 0.26/0.42 % User time : 0.007 s
% 0.26/0.42 % System time : 0.007 s
% 0.26/0.42 % Total time : 0.015 s
% 0.26/0.42 % Maximum resident set size: 4864 pages
% 0.26/0.42 % E exiting
%------------------------------------------------------------------------------