%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU604^2 : 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 : n017.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 08:24:41 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 9 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 250 ( 21 ~; 17 |; 7 &; 168 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
subsetI2: $o ).
thf(decl_27,type,
subsetE: $o ).
thf(decl_28,type,
subsetemptysetimpeq: $o ).
thf(decl_29,type,
setminus: $i > $i > $i ).
thf(decl_30,type,
setminusEL: $o ).
thf(decl_31,type,
setminusER: $o ).
thf(decl_32,type,
esk1_2: $i > $i > $i ).
thf(decl_33,type,
esk2_0: $i ).
thf(decl_34,type,
esk3_0: $i ).
thf(setminusSubset2,conjecture,
( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( setminus @ X1 @ X2 )
= emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHyso4m7z/E---3.1_374643.p',setminusSubset2) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) )
=> ( subset @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHyso4m7z/E---3.1_374643.p',subsetI2) ).
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.WVHyso4m7z/E---3.1_374643.p',subsetE) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
<=> ! [X1: $i] :
( ( subset @ X1 @ emptyset )
=> ( X1 = emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHyso4m7z/E---3.1_374643.p',subsetemptysetimpeq) ).
thf(setminusEL,axiom,
( setminusEL
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHyso4m7z/E---3.1_374643.p',setminusEL) ).
thf(setminusER,axiom,
( setminusER
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
=> ~ ( in @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WVHyso4m7z/E---3.1_374643.p',setminusER) ).
thf(c_0_6,negated_conjecture,
~ ( subsetI2
=> ( subsetE
=> ( subsetemptysetimpeq
=> ( setminusEL
=> ( setminusER
=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( setminus @ X1 @ X2 )
= emptyset ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setminusSubset2]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X19: $i,X20: $i] :
( ! [X21: $i] :
( ( in @ X21 @ X19 )
=> ( in @ X21 @ X20 ) )
=> ( subset @ X19 @ X20 ) )
=> ( ! [X22: $i,X23: $i,X24: $i] :
( ( subset @ X22 @ X23 )
=> ( ( in @ X24 @ X22 )
=> ( in @ X24 @ X23 ) ) )
=> ( ! [X25: $i] :
( ( subset @ X25 @ emptyset )
=> ( X25 = emptyset ) )
=> ( ! [X26: $i,X27: $i,X28: $i] :
( ( in @ X28 @ ( setminus @ X26 @ X27 ) )
=> ( in @ X28 @ X26 ) )
=> ( ! [X29: $i,X30: $i,X31: $i] :
( ( in @ X31 @ ( setminus @ X29 @ X30 ) )
=> ~ ( in @ X31 @ X30 ) )
=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( setminus @ X1 @ X2 )
= emptyset ) ) ) ) ) ) ),
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)],[inference(apply_def,[status(thm)],[c_0_6,subsetI2]),subsetE]),subsetemptysetimpeq]),setminusEL]),setminusER])]) ).
thf(c_0_8,negated_conjecture,
! [X32: $i,X33: $i,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i] :
( ( ( in @ ( esk1_2 @ X32 @ X33 ) @ X32 )
| ( subset @ X32 @ X33 ) )
& ( ~ ( in @ ( esk1_2 @ X32 @ X33 ) @ X33 )
| ( subset @ X32 @ X33 ) )
& ( ~ ( subset @ X35 @ X36 )
| ~ ( in @ X37 @ X35 )
| ( in @ X37 @ X36 ) )
& ( ~ ( subset @ X38 @ emptyset )
| ( X38 = emptyset ) )
& ( ~ ( in @ X41 @ ( setminus @ X39 @ X40 ) )
| ( in @ X41 @ X39 ) )
& ( ~ ( in @ X44 @ ( setminus @ X42 @ X43 ) )
| ~ ( in @ X44 @ X43 ) )
& ( subset @ esk2_0 @ esk3_0 )
& ( ( setminus @ esk2_0 @ esk3_0 )
!= emptyset ) ),
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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
subset @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1 @ ( setminus @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ~ ( in @ X1 @ ( setminus @ X2 @ X3 ) )
| ~ ( in @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ esk3_0 )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( esk1_2 @ ( setminus @ X1 @ X2 ) @ X3 ) @ X1 )
| ( subset @ ( setminus @ X1 @ X2 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( subset @ ( setminus @ X1 @ X2 ) @ X3 )
| ~ ( in @ ( esk1_2 @ ( setminus @ X1 @ X2 ) @ X3 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ ( setminus @ esk2_0 @ X1 ) @ X2 ) @ esk3_0 )
| ( subset @ ( setminus @ esk2_0 @ X1 ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
( ( X1 = emptyset )
| ~ ( subset @ X1 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] : ( subset @ ( setminus @ esk2_0 @ esk3_0 ) @ X1 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
( ( setminus @ esk2_0 @ esk3_0 )
!= emptyset ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU604^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:52:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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.WVHyso4m7z/E---3.1_374643.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho2 with 300s (1) cores
% 0.22/0.27 % post_as_ho3 with pid 374658 completed with status 0
% 0.22/0.27 % Result found by post_as_ho3
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHSF-FFSF22-SFFFMFNN
% 0.22/0.27 % partial match(1): HGUSF-FFSF22-SFFFMFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 374660 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.22/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHSF-FFSF22-SFFFMFNN
% 0.22/0.27 % partial match(1): HGUSF-FFSF22-SFFFMFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 15
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 17
% 0.22/0.27 % Removed in clause preprocessing : 9
% 0.22/0.27 % Initial clauses in saturation : 8
% 0.22/0.27 % Processed clauses : 25
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 2
% 0.22/0.27 % ...remaining for further processing : 23
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 1
% 0.22/0.27 % Backward-rewritten : 1
% 0.22/0.27 % Generated clauses : 33
% 0.22/0.27 % ...of the previous two non-redundant : 23
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 1
% 0.22/0.27 % Paramodulations : 33
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 10
% 0.22/0.27 % ...of those cached : 5
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 21
% 0.22/0.27 % Positive orientable unit clauses : 8
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 2
% 0.22/0.27 % Non-unit-clauses : 11
% 0.22/0.27 % Current number of unprocessed clauses: 5
% 0.22/0.27 % ...number of literals in the above : 9
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 2
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 24
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 19
% 0.22/0.27 % Non-unit clause-clause subsumptions : 3
% 0.22/0.27 % Unit Clause-clause subsumption calls : 16
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 8
% 0.22/0.27 % BW rewrite match successes : 1
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 1521
% 0.22/0.27 % Search garbage collected termcells : 398
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.004 s
% 0.22/0.27 % System time : 0.002 s
% 0.22/0.27 % Total time : 0.006 s
% 0.22/0.27 % Maximum resident set size: 3636 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.006 s
% 0.22/0.27 % System time : 0.006 s
% 0.22/0.27 % Total time : 0.012 s
% 0.22/0.27 % Maximum resident set size: 4608 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------