%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU726^2 : 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 : n014.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 08:25:22 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 0 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 440 ( 43 ~; 38 |; 9 &; 305 @)
% ( 4 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 71 ( 0 ^; 71 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
subsetE: $o ).
thf(decl_27,type,
setminus: $i > $i > $i ).
thf(decl_28,type,
setminusI: $o ).
thf(decl_29,type,
setminusER: $o ).
thf(decl_30,type,
subsetTI: $o ).
thf(decl_31,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(contrasubsetT3,conjecture,
( subsetE
=> ( setminusI
=> ( setminusER
=> ( subsetTI
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ( subset @ ( setminus @ X1 @ X5 ) @ ( setminus @ X1 @ X4 ) )
=> ( subset @ X4 @ X5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uXOOROqz5Z/E---3.1_2727844.p',contrasubsetT3) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uXOOROqz5Z/E---3.1_2727844.p',subsetE) ).
thf(setminusI,axiom,
( setminusI
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uXOOROqz5Z/E---3.1_2727844.p',setminusI) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uXOOROqz5Z/E---3.1_2727844.p',setminusER) ).
thf(subsetTI,axiom,
( subsetTI
<=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X4 )
=> ( in @ X3 @ X5 ) ) )
=> ( subset @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.uXOOROqz5Z/E---3.1_2727844.p',subsetTI) ).
thf(c_0_5,negated_conjecture,
~ ( subsetE
=> ( setminusI
=> ( setminusER
=> ( subsetTI
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ( subset @ ( setminus @ X1 @ X5 ) @ ( setminus @ X1 @ X4 ) )
=> ( subset @ X4 @ X5 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[contrasubsetT3]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i] :
( ( subset @ X22 @ X23 )
=> ( ( in @ X24 @ X22 )
=> ( in @ X24 @ X23 ) ) )
=> ( ! [X25: $i,X26: $i,X27: $i] :
( ( in @ X27 @ X25 )
=> ( ~ ( in @ X27 @ X26 )
=> ( in @ X27 @ ( setminus @ X25 @ X26 ) ) ) )
=> ( ! [X28: $i,X29: $i,X30: $i] :
( ( in @ X30 @ ( setminus @ X28 @ X29 ) )
=> ~ ( in @ X30 @ X29 ) )
=> ( ! [X31: $i,X32: $i] :
( ( in @ X32 @ ( powerset @ X31 ) )
=> ! [X33: $i] :
( ( in @ X33 @ ( powerset @ X31 ) )
=> ( ! [X34: $i] :
( ( in @ X34 @ X31 )
=> ( ( in @ X34 @ X32 )
=> ( in @ X34 @ X33 ) ) )
=> ( subset @ X32 @ X33 ) ) ) )
=> ! [X1: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ ( powerset @ X1 ) )
=> ( ( subset @ ( setminus @ X1 @ X5 ) @ ( setminus @ X1 @ X4 ) )
=> ( subset @ X4 @ X5 ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,subsetE]),setminusI]),setminusER]),subsetTI])]) ).
thf(c_0_7,negated_conjecture,
! [X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i] :
( ( ~ ( subset @ X35 @ X36 )
| ~ ( in @ X37 @ X35 )
| ( in @ X37 @ X36 ) )
& ( ~ ( in @ X40 @ X38 )
| ( in @ X40 @ X39 )
| ( in @ X40 @ ( setminus @ X38 @ X39 ) ) )
& ( ~ ( in @ X43 @ ( setminus @ X41 @ X42 ) )
| ~ ( in @ X43 @ X42 ) )
& ( ( in @ ( esk1_3 @ X44 @ X45 @ X46 ) @ X44 )
| ( subset @ X45 @ X46 )
| ~ ( in @ X46 @ ( powerset @ X44 ) )
| ~ ( in @ X45 @ ( powerset @ X44 ) ) )
& ( ( in @ ( esk1_3 @ X44 @ X45 @ X46 ) @ X45 )
| ( subset @ X45 @ X46 )
| ~ ( in @ X46 @ ( powerset @ X44 ) )
| ~ ( in @ X45 @ ( powerset @ X44 ) ) )
& ( ~ ( in @ ( esk1_3 @ X44 @ X45 @ X46 ) @ X46 )
| ( subset @ X45 @ X46 )
| ~ ( in @ X46 @ ( powerset @ X44 ) )
| ~ ( in @ X45 @ ( powerset @ X44 ) ) )
& ( in @ esk3_0 @ ( powerset @ esk2_0 ) )
& ( in @ esk4_0 @ ( powerset @ esk2_0 ) )
& ( subset @ ( setminus @ esk2_0 @ esk4_0 ) @ ( setminus @ esk2_0 @ esk3_0 ) )
& ~ ( subset @ esk3_0 @ esk4_0 ) ),
inference(distribute,[status(thm)],[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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
subset @ ( setminus @ esk2_0 @ esk4_0 ) @ ( setminus @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( in @ X1 @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ ( setminus @ esk2_0 @ esk3_0 ) )
| ~ ( in @ X1 @ ( setminus @ esk2_0 @ esk4_0 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ ( setminus @ esk2_0 @ esk4_0 ) )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X3 )
| ( in @ X1 @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk4_0 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X2 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_16,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( subset @ X2 @ X3 )
| ~ ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ esk3_0 @ X2 ) @ esk4_0 )
| ( subset @ esk3_0 @ X2 )
| ~ ( in @ ( esk1_3 @ X1 @ esk3_0 @ X2 ) @ esk2_0 )
| ~ ( in @ esk3_0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
~ ( subset @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ~ ( in @ ( esk1_3 @ X1 @ esk3_0 @ esk4_0 ) @ esk2_0 )
| ~ ( in @ esk4_0 @ ( powerset @ X1 ) )
| ~ ( in @ esk3_0 @ ( powerset @ X1 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ( subset @ X2 @ X3 )
| ~ ( in @ X3 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_21,negated_conjecture,
in @ esk4_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_22,negated_conjecture,
in @ esk3_0 @ ( powerset @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU726^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:17:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.uXOOROqz5Z/E---3.1_2727844.p
% 0.08/0.27 % Version: 3.5.1-ho
% 0.08/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.27 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.27 % post_as_ho8 with pid 2727875 completed with status 0
% 0.08/0.27 % Result found by post_as_ho8
% 0.08/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.08/0.27 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.08/0.27 % Search class: HGHNF-FFSS32-SFFFMFNN
% 0.08/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.27 % SubtermCWHack with pid 2727878 completed with status 0
% 0.08/0.27 % Result found by SubtermCWHack
% 0.08/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.08/0.27 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.08/0.27 % Search class: HGHNF-FFSS32-SFFFMFNN
% 0.08/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.27 % Preprocessing time : 0.001 s
% 0.08/0.27
% 0.08/0.27 % Proof found!
% 0.08/0.27 % SZS status Theorem
% 0.08/0.27 % SZS output start CNFRefutation
% See solution above
% 0.08/0.27 % Parsed axioms : 13
% 0.08/0.27 % Removed by relevancy pruning/SinE : 8
% 0.08/0.27 % Initial clauses : 10
% 0.08/0.27 % Removed in clause preprocessing : 0
% 0.08/0.27 % Initial clauses in saturation : 10
% 0.08/0.27 % Processed clauses : 19
% 0.08/0.27 % ...of these trivial : 0
% 0.08/0.27 % ...subsumed : 0
% 0.08/0.27 % ...remaining for further processing : 19
% 0.08/0.27 % Other redundant clauses eliminated : 0
% 0.08/0.27 % Clauses deleted for lack of memory : 0
% 0.08/0.27 % Backward-subsumed : 0
% 0.08/0.27 % Backward-rewritten : 0
% 0.08/0.27 % Generated clauses : 22
% 0.08/0.27 % ...of the previous two non-redundant : 18
% 0.08/0.27 % ...aggressively subsumed : 0
% 0.08/0.27 % Contextual simplify-reflections : 0
% 0.08/0.27 % Paramodulations : 22
% 0.08/0.27 % Factorizations : 0
% 0.08/0.27 % NegExts : 0
% 0.08/0.27 % Equation resolutions : 0
% 0.08/0.27 % Disequality decompositions : 0
% 0.08/0.27 % Total rewrite steps : 2
% 0.08/0.27 % ...of those cached : 0
% 0.08/0.27 % Propositional unsat checks : 0
% 0.08/0.27 % Propositional check models : 0
% 0.08/0.27 % Propositional check unsatisfiable : 0
% 0.08/0.27 % Propositional clauses : 0
% 0.08/0.27 % Propositional clauses after purity: 0
% 0.08/0.27 % Propositional unsat core size : 0
% 0.08/0.27 % Propositional preprocessing time : 0.000
% 0.08/0.27 % Propositional encoding time : 0.000
% 0.08/0.27 % Propositional solver time : 0.000
% 0.08/0.27 % Success case prop preproc time : 0.000
% 0.08/0.27 % Success case prop encoding time : 0.000
% 0.08/0.27 % Success case prop solver time : 0.000
% 0.08/0.27 % Current number of processed clauses : 19
% 0.08/0.27 % Positive orientable unit clauses : 5
% 0.08/0.27 % Positive unorientable unit clauses: 0
% 0.08/0.27 % Negative unit clauses : 1
% 0.08/0.27 % Non-unit-clauses : 13
% 0.08/0.27 % Current number of unprocessed clauses: 9
% 0.08/0.27 % ...number of literals in the above : 38
% 0.08/0.27 % Current number of archived formulas : 0
% 0.08/0.27 % Current number of archived clauses : 0
% 0.08/0.27 % Clause-clause subsumption calls (NU) : 40
% 0.08/0.27 % Rec. Clause-clause subsumption calls : 19
% 0.08/0.27 % Non-unit clause-clause subsumptions : 0
% 0.08/0.27 % Unit Clause-clause subsumption calls : 0
% 0.08/0.27 % Rewrite failures with RHS unbound : 0
% 0.08/0.27 % BW rewrite match attempts : 0
% 0.08/0.27 % BW rewrite match successes : 0
% 0.08/0.27 % Condensation attempts : 0
% 0.08/0.27 % Condensation successes : 0
% 0.08/0.27 % Termbank termtop insertions : 1819
% 0.08/0.27 % Search garbage collected termcells : 500
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.005 s
% 0.08/0.27 % System time : 0.001 s
% 0.08/0.27 % Total time : 0.006 s
% 0.08/0.27 % Maximum resident set size: 3640 pages
% 0.08/0.27
% 0.08/0.27 % -------------------------------------------------
% 0.08/0.27 % User time : 0.005 s
% 0.08/0.27 % System time : 0.007 s
% 0.08/0.27 % Total time : 0.012 s
% 0.08/0.27 % Maximum resident set size: 4864 pages
% 0.08/0.27 % E exiting
%------------------------------------------------------------------------------