%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU585^2 : 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 : n016.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 08:26:48 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 19 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 358 ( 38 ~; 33 |; 11 &; 229 @)
% ( 3 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-3 aty)
% Number of variables : 64 ( 2 ^; 62 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
setunion: $i > $i ).
thf(decl_27,type,
setadjoinE: $o ).
thf(decl_28,type,
setunionE: $o ).
thf(decl_29,type,
uniqinunit: $o ).
thf(decl_30,type,
binunion: $i > $i > $i ).
thf(decl_31,type,
esk1_3: $i > $i > $o > $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(decl_35,type,
epred1_0: $o ).
thf(binunionEcases,conjecture,
( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X2: $i,X5: $i,X1: $i,X4: $o] :
( ( in @ X1 @ ( binunion @ X2 @ X5 ) )
=> ( ( ( in @ X1 @ X2 )
=> X4 )
=> ( ( ( in @ X1 @ X5 )
=> X4 )
=> X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bSF1i7SoA/E---3.1_394555.p',binunionEcases) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X4: $o] :
( ( ( X3 = X1 )
=> X4 )
=> ( ( ( in @ X3 @ X2 )
=> X4 )
=> X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bSF1i7SoA/E---3.1_394555.p',setadjoinE) ).
thf(setunionE,axiom,
( setunionE
<=> ! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X2 ) )
=> ! [X4: $o] :
( ! [X5: $i] :
( ( in @ X1 @ X5 )
=> ( ( in @ X5 @ X2 )
=> X4 ) )
=> X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bSF1i7SoA/E---3.1_394555.p',setunionE) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X1: $i,X3: $i] :
( ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bSF1i7SoA/E---3.1_394555.p',uniqinunit) ).
thf(binunion,axiom,
( binunion
= ( ^ [X1: $i,X3: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3bSF1i7SoA/E---3.1_394555.p',binunion) ).
thf(c_0_5,negated_conjecture,
~ ( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [X2: $i,X5: $i,X1: $i,X4: $o] :
( ( in @ X1 @ ( binunion @ X2 @ X5 ) )
=> ( ( ( in @ X1 @ X2 )
=> X4 )
=> ( ( ( in @ X1 @ X5 )
=> X4 )
=> X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[binunionEcases]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X20: $i,X21: $i,X22: $i] :
( ( in @ X22 @ ( setadjoin @ X20 @ X21 ) )
=> ! [X23: $o] :
( ( ( X22 = X20 )
=> X23 )
=> ( ( ( in @ X22 @ X21 )
=> X23 )
=> X23 ) ) )
=> ( ! [X24: $i,X25: $i] :
( ( in @ X25 @ ( setunion @ X24 ) )
=> ! [X26: $o] :
( ! [X27: $i] :
( ( in @ X25 @ X27 )
=> ( ( in @ X27 @ X24 )
=> X26 ) )
=> X26 ) )
=> ( ! [X28: $i,X29: $i] :
( ( in @ X28 @ ( setadjoin @ X29 @ emptyset ) )
=> ( X28 = X29 ) )
=> ! [X2: $i,X5: $i,X1: $i,X4: $o] :
( ( in @ X1 @ ( binunion @ X2 @ X5 ) )
=> ( ( ( in @ X1 @ X2 )
=> X4 )
=> ( ( ( in @ X1 @ X5 )
=> X4 )
=> X4 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,setadjoinE]),setunionE]),uniqinunit]) ).
thf(c_0_7,negated_conjecture,
! [X34: $i,X35: $i,X36: $i,X37: $o,X38: $i,X39: $i,X40: $o,X42: $i,X43: $i] :
( ( ( in @ X36 @ X35 )
| X37
| ( X36 = X34 )
| ~ ( in @ X36 @ ( setadjoin @ X34 @ X35 ) ) )
& ( ~ X37
| X37
| ( X36 = X34 )
| ~ ( in @ X36 @ ( setadjoin @ X34 @ X35 ) ) )
& ( ( in @ X36 @ X35 )
| X37
| ~ X37
| ~ ( in @ X36 @ ( setadjoin @ X34 @ X35 ) ) )
& ( ~ X37
| X37
| ~ X37
| ~ ( in @ X36 @ ( setadjoin @ X34 @ X35 ) ) )
& ( ( in @ X39 @ ( esk1_3 @ X38 @ X39 @ X40 ) )
| X40
| ~ ( in @ X39 @ ( setunion @ X38 ) ) )
& ( ( in @ ( esk1_3 @ X38 @ X39 @ X40 ) @ X38 )
| X40
| ~ ( in @ X39 @ ( setunion @ X38 ) ) )
& ( ~ X40
| X40
| ~ ( in @ X39 @ ( setunion @ X38 ) ) )
& ( ~ ( in @ X42 @ ( setadjoin @ X43 @ emptyset ) )
| ( X42 = X43 ) )
& ( in @ esk4_0 @ ( binunion @ esk2_0 @ esk3_0 ) )
& ( ~ ( in @ esk4_0 @ esk2_0 )
| epred1_0 )
& ( ~ ( in @ esk4_0 @ esk3_0 )
| epred1_0 )
& ~ epred1_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,plain,
! [X30: $i,X31: $i] :
( ( binunion @ X30 @ X31 )
= ( setunion @ ( setadjoin @ X30 @ ( setadjoin @ X31 @ emptyset ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[binunion])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X2 )
| ( X1 = X3 )
| ~ ( in @ X1 @ ( setadjoin @ X3 @ X2 ) ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7])])]) ).
thf(c_0_10,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_7])])]) ).
thf(c_0_11,plain,
! [X32: $i,X33: $i] :
( ( binunion @ X32 @ X33 )
= ( setunion @ ( setadjoin @ X32 @ ( setadjoin @ X33 @ emptyset ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( esk1_3 @ ( setadjoin @ X1 @ X2 ) @ X3 @ ~ $true )
= X1 )
| ( in @ ( esk1_3 @ ( setadjoin @ X1 @ X2 ) @ X3 @ ~ $true ) @ X2 )
| ~ ( in @ X3 @ ( setunion @ ( setadjoin @ X1 @ X2 ) ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X1: $i,X2: $i] :
( ( binunion @ X1 @ X2 )
= ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( esk1_3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 @ ~ $true )
= X1 )
| ( ( esk1_3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ X3 @ ~ $true )
= X2 )
| ~ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
in @ esk4_0 @ ( binunion @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_17,negated_conjecture,
( epred1_0
| ~ ( in @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_19,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_7])])]) ).
thf(c_0_20,negated_conjecture,
( ( ( esk1_3 @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk4_0 @ ~ $true )
= esk3_0 )
| ( ( esk1_3 @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk4_0 @ ~ $true )
= esk2_0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_21,negated_conjecture,
~ ( in @ esk4_0 @ esk3_0 ),
inference(sr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,negated_conjecture,
( epred1_0
| ~ ( in @ esk4_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_23,negated_conjecture,
( ( esk1_3 @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk4_0 @ ~ $true )
= esk2_0 ),
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_14]),c_0_16])]),c_0_21]) ).
thf(c_0_24,negated_conjecture,
~ ( in @ esk4_0 @ esk2_0 ),
inference(sr,[status(thm)],[c_0_22,c_0_18]) ).
thf(c_0_25,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_23]),c_0_14]),c_0_16])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU585^2 : 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 : n016.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 13:57:34 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 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.3bSF1i7SoA/E---3.1_394555.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.22/0.27 % Starting lpo1_def_fix with 300s (1) cores
% 0.22/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.22/0.27 % new_ho_10 with pid 394595 completed with status 0
% 0.22/0.27 % Result found by new_ho_10
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) 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: HGUSF-FFSF32-MSFFMFNN
% 0.22/0.27 % partial match(1): HGUSF-FFSF32-MHFFMFNN
% 0.22/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.27 % Starting sh5l with 151s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 151s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 146s (1) cores
% 0.22/0.27 % new_ho_10 with pid 394604 completed with status 0
% 0.22/0.27 % Result found by new_ho_10
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) 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: HGUSF-FFSF32-MSFFMFNN
% 0.22/0.27 % partial match(1): HGUSF-FFSF32-MHFFMFNN
% 0.22/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27 % Presaturation interreduction done
% 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 : 13
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 21
% 0.22/0.27 % Removed in clause preprocessing : 12
% 0.22/0.27 % Initial clauses in saturation : 9
% 0.22/0.27 % Processed clauses : 34
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 34
% 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 : 0
% 0.22/0.27 % Backward-rewritten : 1
% 0.22/0.27 % Generated clauses : 64
% 0.22/0.27 % ...of the previous two non-redundant : 63
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 63
% 0.22/0.27 % Factorizations : 1
% 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 : 12
% 0.22/0.27 % ...of those cached : 8
% 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 : 24
% 0.22/0.27 % Positive orientable unit clauses : 3
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 3
% 0.22/0.27 % Non-unit-clauses : 18
% 0.22/0.27 % Current number of unprocessed clauses: 46
% 0.22/0.27 % ...number of literals in the above : 150
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 10
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 130
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 123
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 2
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 1
% 0.22/0.27 % BW rewrite match successes : 1
% 0.22/0.27 % Condensation attempts : 34
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 3262
% 0.22/0.27 % Search garbage collected termcells : 454
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.007 s
% 0.22/0.27 % System time : 0.004 s
% 0.22/0.27 % Total time : 0.011 s
% 0.22/0.27 % Maximum resident set size: 3640 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.026 s
% 0.22/0.27 % System time : 0.019 s
% 0.22/0.27 % Total time : 0.045 s
% 0.22/0.27 % Maximum resident set size: 4608 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------