%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU815^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:25:45 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 142 ( 3 equ; 0 cnn)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 454 ( 50 ~; 46 |; 10 &; 295 @)
% ( 4 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 90 ( 2 ^; 88 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
setunion: $i > $i ).
thf(decl_25,type,
setunionI: $o ).
thf(decl_26,type,
setunionE: $o ).
thf(decl_27,type,
subset: $i > $i > $o ).
thf(decl_28,type,
subsetI1: $o ).
thf(decl_29,type,
transitiveset: $i > $o ).
thf(decl_30,type,
transitivesetOp2: $o ).
thf(decl_31,type,
esk1_3: $i > $i > $o > $i ).
thf(decl_32,type,
esk2_2: $i > $i > $i ).
thf(decl_33,type,
esk3_1: $i > $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(decl_35,type,
esk5_0: $i ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [X1: $i] :
! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( subset @ X5 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p',transitiveset) ).
thf(setunionTransitive,conjecture,
( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( transitiveset @ X2 ) )
=> ( transitiveset @ ( setunion @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p',setunionTransitive) ).
thf(transitivesetOp2,axiom,
( transitivesetOp2
<=> ! [X5: $i] :
( ( transitiveset @ X5 )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X5 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p',transitivesetOp2) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p',setunionI) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
=> ! [X4: $o] :
( ! [X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> X4 ) )
=> X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p',setunionE) ).
thf(subsetI1,axiom,
( subsetI1
<=> ! [X1: $i,X3: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X3 ) )
=> ( subset @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p',subsetI1) ).
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,
~ ( setunionI
=> ( setunionE
=> ( subsetI1
=> ( transitivesetOp2
=> ! [X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ( transitiveset @ X2 ) )
=> ( transitiveset @ ( setunion @ X5 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setunionTransitive]) ).
thf(c_0_8,axiom,
( transitivesetOp2
= ( ! [X5: $i] :
( ! [X21: $i] :
( ( in @ X21 @ X5 )
=> ( subset @ X21 @ X5 ) )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X5 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X5 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[transitivesetOp2,c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i] :
( ( in @ X23 @ X24 )
=> ( ( in @ X24 @ X22 )
=> ( in @ X23 @ ( setunion @ X22 ) ) ) )
=> ( ! [X25: $i,X26: $i] :
( ( in @ X26 @ ( setunion @ X25 ) )
=> ! [X27: $o] :
( ! [X28: $i] :
( ( in @ X26 @ X28 )
=> ( ( in @ X28 @ X25 )
=> X27 ) )
=> X27 ) )
=> ( ! [X29: $i,X30: $i] :
( ! [X31: $i] :
( ( in @ X31 @ X29 )
=> ( in @ X31 @ X30 ) )
=> ( subset @ X29 @ X30 ) )
=> ( ! [X32: $i] :
( ! [X33: $i] :
( ( in @ X33 @ X32 )
=> ( subset @ X33 @ X32 ) )
=> ! [X34: $i,X35: $i] :
( ( in @ X34 @ X32 )
=> ( ( in @ X35 @ X34 )
=> ( in @ X35 @ X32 ) ) ) )
=> ! [X5: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X5 )
=> ! [X36: $i] :
( ( in @ X36 @ X2 )
=> ( subset @ X36 @ X2 ) ) )
=> ! [X37: $i] :
( ( in @ X37 @ ( setunion @ X5 ) )
=> ( subset @ X37 @ ( setunion @ X5 ) ) ) ) ) ) ) ),
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,setunionI]),setunionE]),subsetI1]),c_0_6]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $o,X45: $i,X46: $i,X48: $i,X50: $i,X51: $i,X53: $i,X54: $i] :
( ( ~ ( in @ X39 @ X40 )
| ~ ( in @ X40 @ X38 )
| ( in @ X39 @ ( setunion @ X38 ) ) )
& ( ( in @ X42 @ ( esk1_3 @ X41 @ X42 @ X43 ) )
| X43
| ~ ( in @ X42 @ ( setunion @ X41 ) ) )
& ( ( in @ ( esk1_3 @ X41 @ X42 @ X43 ) @ X41 )
| X43
| ~ ( in @ X42 @ ( setunion @ X41 ) ) )
& ( ~ X43
| X43
| ~ ( in @ X42 @ ( setunion @ X41 ) ) )
& ( ( in @ ( esk2_2 @ X45 @ X46 ) @ X45 )
| ( subset @ X45 @ X46 ) )
& ( ~ ( in @ ( esk2_2 @ X45 @ X46 ) @ X46 )
| ( subset @ X45 @ X46 ) )
& ( ( in @ ( esk3_1 @ X48 ) @ X48 )
| ~ ( in @ X50 @ X48 )
| ~ ( in @ X51 @ X50 )
| ( in @ X51 @ X48 ) )
& ( ~ ( subset @ ( esk3_1 @ X48 ) @ X48 )
| ~ ( in @ X50 @ X48 )
| ~ ( in @ X51 @ X50 )
| ( in @ X51 @ X48 ) )
& ( ~ ( in @ X53 @ esk4_0 )
| ~ ( in @ X54 @ X53 )
| ( subset @ X54 @ X53 ) )
& ( in @ esk5_0 @ ( setunion @ esk4_0 ) )
& ~ ( subset @ esk5_0 @ ( setunion @ 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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X3 @ X1 )
| ~ ( subset @ ( esk3_1 @ X1 ) @ X1 )
| ~ ( in @ X2 @ X1 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X2: $i,X1: $i] :
( ( subset @ X2 @ X1 )
| ~ ( in @ X1 @ esk4_0 )
| ~ ( in @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk3_1 @ X1 ) @ X1 )
| ( in @ X3 @ X1 )
| ~ ( in @ X2 @ X1 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ X1 @ X3 )
| ~ ( in @ X3 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ ~ $true ) @ X1 )
| ~ ( in @ X2 @ ( setunion @ X1 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10])])]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( esk1_3 @ esk4_0 @ X2 @ ~ $true ) )
| ~ ( in @ X3 @ ( esk1_3 @ esk4_0 @ X2 @ ~ $true ) )
| ~ ( in @ X2 @ ( setunion @ esk4_0 ) )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( esk1_3 @ X2 @ X1 @ ~ $true ) )
| ~ ( in @ X1 @ ( setunion @ X2 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_10])])]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ ( setunion @ X2 ) )
| ~ ( in @ X1 @ ( esk1_3 @ X2 @ X3 @ ~ $true ) )
| ~ ( in @ X3 @ ( setunion @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( esk1_3 @ esk4_0 @ X2 @ ~ $true ) )
| ~ ( in @ X2 @ ( setunion @ esk4_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setunion @ esk4_0 ) )
| ~ ( in @ X2 @ ( setunion @ esk4_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
in @ esk5_0 @ ( setunion @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk2_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ ( setunion @ esk4_0 ) )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( subset @ X1 @ ( setunion @ esk4_0 ) )
| ~ ( in @ ( esk2_2 @ X1 @ ( setunion @ esk4_0 ) ) @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk2_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_27,negated_conjecture,
~ ( subset @ esk5_0 @ ( setunion @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU815^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % 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 14:34:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.mloVzljkkX/E---3.1_4085206.p
% 0.23/0.30 % Version: 3.5.1-ho
% 0.23/0.30 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.23/0.30 % Starting lpo1_def_fix with 300s (1) cores
% 0.23/0.30 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.23/0.30 % new_ho_10 with pid 4085219 completed with status 0
% 0.23/0.30 % Result found by new_ho_10
% 0.23/0.30 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.30 % No SInE strategy applied
% 0.23/0.30 % Search class: HGUNF-FFSF31-SSFFMFNN
% 0.23/0.30 % partial match(2): HGUNF-FFSF21-SFFFMFNN
% 0.23/0.30 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.30 % Starting SubtermCWHack with 151s (1) cores
% 0.23/0.30 % Starting new_ho_10 with 901s (1) cores
% 0.23/0.30 % Starting sh5l with 151s (1) cores
% 0.23/0.30 % Starting new_bool_1 with 151s (1) cores
% 0.23/0.30 % Starting new_bool_2 with 146s (1) cores
% 0.23/0.30 % new_ho_10 with pid 4085227 completed with status 0
% 0.23/0.30 % Result found by new_ho_10
% 0.23/0.30 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.23/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.30 % Starting new_ho_10 with 1500s (5) cores
% 0.23/0.30 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.30 % No SInE strategy applied
% 0.23/0.30 % Search class: HGUNF-FFSF31-SSFFMFNN
% 0.23/0.30 % partial match(2): HGUNF-FFSF21-SFFFMFNN
% 0.23/0.30 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.30 % Starting SubtermCWHack with 151s (1) cores
% 0.23/0.30 % Starting new_ho_10 with 901s (1) cores
% 0.23/0.30 % Preprocessing time : 0.001 s
% 0.23/0.30 % Presaturation interreduction done
% 0.23/0.30
% 0.23/0.30 % Proof found!
% 0.23/0.30 % SZS status Theorem
% 0.23/0.30 % SZS output start CNFRefutation
% See solution above
% 0.23/0.30 % Parsed axioms : 14
% 0.23/0.30 % Removed by relevancy pruning/SinE : 0
% 0.23/0.30 % Initial clauses : 19
% 0.23/0.30 % Removed in clause preprocessing : 9
% 0.23/0.30 % Initial clauses in saturation : 10
% 0.23/0.30 % Processed clauses : 96
% 0.23/0.30 % ...of these trivial : 1
% 0.23/0.30 % ...subsumed : 3
% 0.23/0.30 % ...remaining for further processing : 92
% 0.23/0.30 % Other redundant clauses eliminated : 0
% 0.23/0.30 % Clauses deleted for lack of memory : 0
% 0.23/0.30 % Backward-subsumed : 1
% 0.23/0.30 % Backward-rewritten : 1
% 0.23/0.30 % Generated clauses : 486
% 0.23/0.30 % ...of the previous two non-redundant : 460
% 0.23/0.30 % ...aggressively subsumed : 0
% 0.23/0.30 % Contextual simplify-reflections : 1
% 0.23/0.30 % Paramodulations : 486
% 0.23/0.30 % Factorizations : 0
% 0.23/0.30 % NegExts : 0
% 0.23/0.30 % Equation resolutions : 0
% 0.23/0.30 % Disequality decompositions : 0
% 0.23/0.30 % Total rewrite steps : 30
% 0.23/0.30 % ...of those cached : 28
% 0.23/0.30 % Propositional unsat checks : 0
% 0.23/0.30 % Propositional check models : 0
% 0.23/0.30 % Propositional check unsatisfiable : 0
% 0.23/0.30 % Propositional clauses : 0
% 0.23/0.30 % Propositional clauses after purity: 0
% 0.23/0.30 % Propositional unsat core size : 0
% 0.23/0.30 % Propositional preprocessing time : 0.000
% 0.23/0.30 % Propositional encoding time : 0.000
% 0.23/0.30 % Propositional solver time : 0.000
% 0.23/0.30 % Success case prop preproc time : 0.000
% 0.23/0.30 % Success case prop encoding time : 0.000
% 0.23/0.30 % Success case prop solver time : 0.000
% 0.23/0.30 % Current number of processed clauses : 80
% 0.23/0.30 % Positive orientable unit clauses : 4
% 0.23/0.30 % Positive unorientable unit clauses: 0
% 0.23/0.30 % Negative unit clauses : 2
% 0.23/0.30 % Non-unit-clauses : 74
% 0.23/0.30 % Current number of unprocessed clauses: 382
% 0.23/0.30 % ...number of literals in the above : 1835
% 0.23/0.30 % Current number of archived formulas : 0
% 0.23/0.30 % Current number of archived clauses : 12
% 0.23/0.30 % Clause-clause subsumption calls (NU) : 949
% 0.23/0.30 % Rec. Clause-clause subsumption calls : 596
% 0.23/0.30 % Non-unit clause-clause subsumptions : 4
% 0.23/0.30 % Unit Clause-clause subsumption calls : 4
% 0.23/0.30 % Rewrite failures with RHS unbound : 0
% 0.23/0.30 % BW rewrite match attempts : 4
% 0.23/0.30 % BW rewrite match successes : 1
% 0.23/0.30 % Condensation attempts : 96
% 0.23/0.30 % Condensation successes : 0
% 0.23/0.30 % Termbank termtop insertions : 13835
% 0.23/0.30 % Search garbage collected termcells : 590
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.025 s
% 0.23/0.30 % System time : 0.006 s
% 0.23/0.30 % Total time : 0.030 s
% 0.23/0.30 % Maximum resident set size: 3640 pages
% 0.23/0.30
% 0.23/0.30 % -------------------------------------------------
% 0.23/0.30 % User time : 0.093 s
% 0.23/0.30 % System time : 0.020 s
% 0.23/0.30 % Total time : 0.113 s
% 0.23/0.30 % Maximum resident set size: 4864 pages
% 0.23/0.30 % E exiting
%------------------------------------------------------------------------------