%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU742^2 : 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 : n015.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 08:25:27 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 117 ( 0 equ; 0 cnn)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 490 ( 41 ~; 35 |; 8 &; 355 @)
% ( 3 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 73 !; 0 ?; 73 :)
% 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,
binintersectI: $o ).
thf(decl_28,type,
inIntersectImpInUnion: $o ).
thf(decl_29,type,
inIntersectImpInUnion2: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(decl_34,type,
esk5_0: $i ).
thf(inIntersectImpInIntersectUnions,conjecture,
( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X3 @ ( binintersect @ ( binunion @ X4 @ X6 ) @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4Q4bkXVJbK/E---3.1_3597850.p',inIntersectImpInIntersectUnions) ).
thf(binintersectI,axiom,
( binintersectI
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4Q4bkXVJbK/E---3.1_3597850.p',binintersectI) ).
thf(inIntersectImpInUnion,axiom,
( inIntersectImpInUnion
<=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X3 @ ( binunion @ X4 @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4Q4bkXVJbK/E---3.1_3597850.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,axiom,
( inIntersectImpInUnion2
<=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X3 @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4Q4bkXVJbK/E---3.1_3597850.p',inIntersectImpInUnion2) ).
thf(c_0_4,negated_conjecture,
~ ( binintersectI
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X3 @ ( binintersect @ ( binunion @ X4 @ X6 ) @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[inIntersectImpInIntersectUnions]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X25: $i,X26: $i,X27: $i] :
( ( in @ X27 @ X25 )
=> ( ( in @ X27 @ X26 )
=> ( in @ X27 @ ( binintersect @ X25 @ X26 ) ) ) )
=> ( ! [X28: $i,X29: $i] :
( ( in @ X29 @ ( powerset @ X28 ) )
=> ! [X30: $i] :
( ( in @ X30 @ ( powerset @ X28 ) )
=> ! [X31: $i] :
( ( in @ X31 @ ( powerset @ X28 ) )
=> ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ( ( in @ X32 @ ( binintersect @ X29 @ X30 ) )
=> ( in @ X32 @ ( binunion @ X29 @ X31 ) ) ) ) ) ) )
=> ( ! [X33: $i,X34: $i] :
( ( in @ X34 @ ( powerset @ X33 ) )
=> ! [X35: $i] :
( ( in @ X35 @ ( powerset @ X33 ) )
=> ! [X36: $i] :
( ( in @ X36 @ ( powerset @ X33 ) )
=> ! [X37: $i] :
( ( in @ X37 @ X33 )
=> ( ( in @ X37 @ ( binintersect @ X34 @ X35 ) )
=> ( in @ X37 @ ( binunion @ X35 @ X36 ) ) ) ) ) ) )
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ! [X6: $i] :
( ( in @ X6 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( binintersect @ X4 @ X5 ) )
=> ( in @ X3 @ ( binintersect @ ( binunion @ X4 @ X6 ) @ ( binunion @ X5 @ X6 ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,binintersectI]),inIntersectImpInUnion]),inIntersectImpInUnion2]) ).
thf(c_0_6,negated_conjecture,
! [X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X50: $i] :
( ( ~ ( in @ X40 @ X38 )
| ~ ( in @ X40 @ X39 )
| ( in @ X40 @ ( binintersect @ X38 @ X39 ) ) )
& ( ~ ( in @ X42 @ ( powerset @ X41 ) )
| ~ ( in @ X43 @ ( powerset @ X41 ) )
| ~ ( in @ X44 @ ( powerset @ X41 ) )
| ~ ( in @ X45 @ X41 )
| ~ ( in @ X45 @ ( binintersect @ X42 @ X43 ) )
| ( in @ X45 @ ( binunion @ X42 @ X44 ) ) )
& ( ~ ( in @ X47 @ ( powerset @ X46 ) )
| ~ ( in @ X48 @ ( powerset @ X46 ) )
| ~ ( in @ X49 @ ( powerset @ X46 ) )
| ~ ( in @ X50 @ X46 )
| ~ ( in @ X50 @ ( binintersect @ X47 @ X48 ) )
| ( in @ X50 @ ( binunion @ X48 @ X49 ) ) )
& ( in @ esk2_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk3_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk1_0 ) )
& ( in @ esk5_0 @ esk1_0 )
& ( in @ esk5_0 @ ( binintersect @ esk2_0 @ esk3_0 ) )
& ~ ( in @ esk5_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk4_0 ) @ ( binunion @ esk3_0 @ esk4_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,
! [X2: $i,X1: $i,X4: $i,X5: $i,X3: $i] :
( ( in @ X5 @ ( binunion @ X3 @ X4 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X5 @ X2 )
| ~ ( in @ X5 @ ( binintersect @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
in @ esk5_0 @ ( binintersect @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( in @ esk5_0 @ ( binintersect @ ( binunion @ esk2_0 @ esk4_0 ) @ ( binunion @ esk3_0 @ esk4_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( binintersect @ X2 @ X3 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ esk5_0 @ ( binunion @ esk3_0 @ X1 ) )
| ~ ( in @ esk3_0 @ ( powerset @ X2 ) )
| ~ ( in @ esk2_0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ esk5_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
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,
in @ esk5_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i,X1: $i,X4: $i,X5: $i,X3: $i] :
( ( in @ X5 @ ( binunion @ X1 @ X4 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X3 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X5 @ X2 )
| ~ ( in @ X5 @ ( binintersect @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
( ~ ( in @ esk5_0 @ ( binunion @ esk3_0 @ esk4_0 ) )
| ~ ( in @ esk5_0 @ ( binunion @ esk2_0 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( in @ esk5_0 @ ( binunion @ esk3_0 @ X1 ) )
| ~ ( in @ X1 @ ( powerset @ esk1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]) ).
thf(c_0_18,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ esk5_0 @ ( binunion @ esk2_0 @ X1 ) )
| ~ ( in @ esk3_0 @ ( powerset @ X2 ) )
| ~ ( in @ esk2_0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ esk5_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
thf(c_0_20,negated_conjecture,
~ ( in @ esk5_0 @ ( binunion @ esk2_0 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i] :
( ( in @ esk5_0 @ ( binunion @ esk2_0 @ X1 ) )
| ~ ( in @ X1 @ ( powerset @ esk1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_13]),c_0_14])]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU742^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:22:47 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.4Q4bkXVJbK/E---3.1_3597850.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.07/0.26 % post_as_ho8 with pid 3597864 completed with status 0
% 0.07/0.26 % Result found by post_as_ho8
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.07/0.26 % Search class: HHUNF-FFSS21-SFFFMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 3597867 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.07/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.07/0.26 % Search class: HHUNF-FFSS21-SFFFMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 11
% 0.07/0.26 % Removed by relevancy pruning/SinE : 7
% 0.07/0.26 % Initial clauses : 9
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 9
% 0.07/0.26 % Processed clauses : 15
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 15
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 1
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 9
% 0.07/0.26 % ...of the previous two non-redundant : 8
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 9
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 6
% 0.07/0.26 % ...of those cached : 3
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 14
% 0.07/0.26 % Positive orientable unit clauses : 5
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 2
% 0.07/0.26 % Non-unit-clauses : 7
% 0.07/0.26 % Current number of unprocessed clauses: 2
% 0.07/0.26 % ...number of literals in the above : 14
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 1
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 7
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 4
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 2
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 0
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 1742
% 0.07/0.26 % Search garbage collected termcells : 506
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.003 s
% 0.07/0.26 % System time : 0.002 s
% 0.07/0.26 % Total time : 0.005 s
% 0.07/0.26 % Maximum resident set size: 3640 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.005 s
% 0.07/0.26 % System time : 0.006 s
% 0.07/0.26 % Total time : 0.011 s
% 0.07/0.26 % Maximum resident set size: 4608 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------