%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU813^2 : 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 : n020.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 08:25:44 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 97 ( 3 equ; 0 cnn)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 281 ( 22 ~; 17 |; 8 &; 191 @)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 2 ^; 61 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
binintersect: $i > $i > $i ).
thf(decl_26,type,
binintersectSubset5: $o ).
thf(decl_27,type,
binintersectEL: $o ).
thf(decl_28,type,
binintersectER: $o ).
thf(decl_29,type,
transitiveset: $i > $o ).
thf(decl_30,type,
transitivesetOp1: $o ).
thf(decl_31,type,
esk1_1: $i > $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [X1: $i] :
! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( subset @ X5 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OUYI4FgrJg/E---3.1_1136982.p',transitiveset) ).
thf(binintTransitive,conjecture,
( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X5: $i] :
( ( transitiveset @ X5 )
=> ! [X6: $i] :
( ( transitiveset @ X6 )
=> ( transitiveset @ ( binintersect @ X5 @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OUYI4FgrJg/E---3.1_1136982.p',binintTransitive) ).
thf(transitivesetOp1,axiom,
( transitivesetOp1
<=> ! [X5: $i] :
( ( transitiveset @ X5 )
=> ! [X1: $i] :
( ( in @ X1 @ X5 )
=> ( subset @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OUYI4FgrJg/E---3.1_1136982.p',transitivesetOp1) ).
thf(binintersectSubset5,axiom,
( binintersectSubset5
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X3 @ X1 )
=> ( ( subset @ X3 @ X2 )
=> ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OUYI4FgrJg/E---3.1_1136982.p',binintersectSubset5) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OUYI4FgrJg/E---3.1_1136982.p',binintersectEL) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X4 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.OUYI4FgrJg/E---3.1_1136982.p',binintersectER) ).
thf(c_0_6,plain,
( transitiveset
= ( ^ [Z0: $i] :
! [X5: $i] :
( ( in @ X5 @ Z0 )
=> ( subset @ X5 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitiveset]) ).
thf(c_0_7,negated_conjecture,
~ ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectER
=> ( transitivesetOp1
=> ! [X5: $i] :
( ( transitiveset @ X5 )
=> ! [X6: $i] :
( ( transitiveset @ X6 )
=> ( transitiveset @ ( binintersect @ X5 @ X6 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binintTransitive]) ).
thf(c_0_8,axiom,
( transitivesetOp1
= ( ! [X5: $i] :
( ! [X20: $i] :
( ( in @ X20 @ X5 )
=> ( subset @ X20 @ X5 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X5 )
=> ( subset @ X1 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[transitivesetOp1,c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X21: $i,X22: $i,X23: $i] :
( ( subset @ X23 @ X21 )
=> ( ( subset @ X23 @ X22 )
=> ( subset @ X23 @ ( binintersect @ X21 @ X22 ) ) ) )
=> ( ! [X24: $i,X25: $i,X26: $i] :
( ( in @ X26 @ ( binintersect @ X24 @ X25 ) )
=> ( in @ X26 @ X24 ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( in @ X29 @ ( binintersect @ X27 @ X28 ) )
=> ( in @ X29 @ X28 ) )
=> ( ! [X30: $i] :
( ! [X31: $i] :
( ( in @ X31 @ X30 )
=> ( subset @ X31 @ X30 ) )
=> ! [X32: $i] :
( ( in @ X32 @ X30 )
=> ( subset @ X32 @ X30 ) ) )
=> ! [X5: $i] :
( ! [X33: $i] :
( ( in @ X33 @ X5 )
=> ( subset @ X33 @ X5 ) )
=> ! [X6: $i] :
( ! [X34: $i] :
( ( in @ X34 @ X6 )
=> ( subset @ X34 @ X6 ) )
=> ! [X35: $i] :
( ( in @ X35 @ ( binintersect @ X5 @ X6 ) )
=> ( subset @ X35 @ ( binintersect @ X5 @ X6 ) ) ) ) ) ) ) ) ),
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_7,binintersectSubset5]),binintersectEL]),c_0_8]),c_0_6]),binintersectER]) ).
thf(c_0_10,negated_conjecture,
! [X36: $i,X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X47: $i,X49: $i,X51: $i] :
( ( ~ ( subset @ X38 @ X36 )
| ~ ( subset @ X38 @ X37 )
| ( subset @ X38 @ ( binintersect @ X36 @ X37 ) ) )
& ( ~ ( in @ X41 @ ( binintersect @ X39 @ X40 ) )
| ( in @ X41 @ X39 ) )
& ( ~ ( in @ X44 @ ( binintersect @ X42 @ X43 ) )
| ( in @ X44 @ X43 ) )
& ( ( in @ ( esk1_1 @ X45 ) @ X45 )
| ~ ( in @ X47 @ X45 )
| ( subset @ X47 @ X45 ) )
& ( ~ ( subset @ ( esk1_1 @ X45 ) @ X45 )
| ~ ( in @ X47 @ X45 )
| ( subset @ X47 @ X45 ) )
& ( ~ ( in @ X49 @ esk2_0 )
| ( subset @ X49 @ esk2_0 ) )
& ( ~ ( in @ X51 @ esk3_0 )
| ( subset @ X51 @ esk3_0 ) )
& ( in @ esk4_0 @ ( binintersect @ esk2_0 @ esk3_0 ) )
& ~ ( subset @ esk4_0 @ ( binintersect @ esk2_0 @ esk3_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_9])])])])])]) ).
thf(c_0_11,negated_conjecture,
~ ( subset @ esk4_0 @ ( binintersect @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ ( binintersect @ X2 @ X3 ) )
| ~ ( subset @ X1 @ X2 )
| ~ ( subset @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( binintersect @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
in @ esk4_0 @ ( binintersect @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
( ~ ( subset @ esk4_0 @ esk3_0 )
| ~ ( subset @ esk4_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( subset @ X1 @ esk3_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,negated_conjecture,
in @ esk4_0 @ esk3_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1 @ ( binintersect @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,negated_conjecture,
~ ( subset @ esk4_0 @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( subset @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,negated_conjecture,
in @ esk4_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU813^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n020.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:34:34 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.30 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.OUYI4FgrJg/E---3.1_1136982.p
% 0.24/0.33 % Version: 3.5.1-ho
% 0.24/0.33 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.33 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.33 % Starting lpo1_def_fix with 300s (1) cores
% 0.24/0.33 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.24/0.33 % lpo1_def_fix with pid 1136997 completed with status 0
% 0.24/0.33 % Result found by lpo1_def_fix
% 0.24/0.33 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.33 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.33 % Starting lpo1_def_fix with 300s (1) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.24/0.33 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.24/0.33 % Search class: HGUNF-FFSF21-SSFFMFNN
% 0.24/0.33 % partial match(1): HGUNF-FFSF21-SFFFMFNN
% 0.24/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.33 % SubtermCWHack with pid 1137002 completed with status 0
% 0.24/0.33 % Result found by SubtermCWHack
% 0.24/0.33 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.24/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.33 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.33 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.33 % Starting lpo1_def_fix with 300s (1) cores
% 0.24/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.24/0.33 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.24/0.33 % Search class: HGUNF-FFSF21-SSFFMFNN
% 0.24/0.33 % partial match(1): HGUNF-FFSF21-SFFFMFNN
% 0.24/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.33 % Preprocessing time : 0.002 s
% 0.24/0.33
% 0.24/0.33 % Proof found!
% 0.24/0.33 % SZS status Theorem
% 0.24/0.33 % SZS output start CNFRefutation
% See solution above
% 0.24/0.33 % Parsed axioms : 14
% 0.24/0.33 % Removed by relevancy pruning/SinE : 8
% 0.24/0.33 % Initial clauses : 9
% 0.24/0.33 % Removed in clause preprocessing : 0
% 0.24/0.33 % Initial clauses in saturation : 9
% 0.24/0.33 % Processed clauses : 23
% 0.24/0.33 % ...of these trivial : 0
% 0.24/0.33 % ...subsumed : 3
% 0.24/0.33 % ...remaining for further processing : 20
% 0.24/0.33 % Other redundant clauses eliminated : 0
% 0.24/0.33 % Clauses deleted for lack of memory : 0
% 0.24/0.33 % Backward-subsumed : 1
% 0.24/0.33 % Backward-rewritten : 0
% 0.24/0.33 % Generated clauses : 19
% 0.24/0.33 % ...of the previous two non-redundant : 17
% 0.24/0.33 % ...aggressively subsumed : 0
% 0.24/0.33 % Contextual simplify-reflections : 0
% 0.24/0.33 % Paramodulations : 18
% 0.24/0.33 % Factorizations : 0
% 0.24/0.33 % NegExts : 0
% 0.24/0.33 % Equation resolutions : 0
% 0.24/0.33 % Disequality decompositions : 0
% 0.24/0.33 % Total rewrite steps : 3
% 0.24/0.33 % ...of those cached : 0
% 0.24/0.33 % Propositional unsat checks : 0
% 0.24/0.33 % Propositional check models : 0
% 0.24/0.33 % Propositional check unsatisfiable : 0
% 0.24/0.33 % Propositional clauses : 0
% 0.24/0.33 % Propositional clauses after purity: 0
% 0.24/0.33 % Propositional unsat core size : 0
% 0.24/0.33 % Propositional preprocessing time : 0.000
% 0.24/0.33 % Propositional encoding time : 0.000
% 0.24/0.33 % Propositional solver time : 0.000
% 0.24/0.33 % Success case prop preproc time : 0.000
% 0.24/0.33 % Success case prop encoding time : 0.000
% 0.24/0.33 % Success case prop solver time : 0.000
% 0.24/0.33 % Current number of processed clauses : 18
% 0.24/0.33 % Positive orientable unit clauses : 6
% 0.24/0.33 % Positive unorientable unit clauses: 0
% 0.24/0.33 % Negative unit clauses : 2
% 0.24/0.33 % Non-unit-clauses : 10
% 0.24/0.33 % Current number of unprocessed clauses: 2
% 0.24/0.33 % ...number of literals in the above : 7
% 0.24/0.33 % Current number of archived formulas : 0
% 0.24/0.33 % Current number of archived clauses : 2
% 0.24/0.33 % Clause-clause subsumption calls (NU) : 9
% 0.24/0.33 % Rec. Clause-clause subsumption calls : 9
% 0.24/0.33 % Non-unit clause-clause subsumptions : 3
% 0.24/0.33 % Unit Clause-clause subsumption calls : 2
% 0.24/0.33 % Rewrite failures with RHS unbound : 0
% 0.24/0.33 % BW rewrite match attempts : 0
% 0.24/0.33 % BW rewrite match successes : 0
% 0.24/0.33 % Condensation attempts : 0
% 0.24/0.33 % Condensation successes : 0
% 0.24/0.33 % Termbank termtop insertions : 1479
% 0.24/0.33 % Search garbage collected termcells : 489
% 0.24/0.33
% 0.24/0.33 % -------------------------------------------------
% 0.24/0.33 % User time : 0.008 s
% 0.24/0.33 % System time : 0.002 s
% 0.24/0.33 % Total time : 0.010 s
% 0.24/0.33 % Maximum resident set size: 3640 pages
% 0.24/0.33
% 0.24/0.33 % -------------------------------------------------
% 0.24/0.33 % User time : 0.010 s
% 0.24/0.33 % System time : 0.006 s
% 0.24/0.33 % Total time : 0.016 s
% 0.24/0.33 % Maximum resident set size: 4864 pages
% 0.24/0.33 % E exiting
%------------------------------------------------------------------------------