%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU585^2 : 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 : n008.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 08:24:36 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 17 equ; 0 cnn)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 354 ( 38 ~; 33 |; 11 &; 225 @)
% ( 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 : 60 ( 4 ^; 56 !; 0 ?; 60 :)
% 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/sandbox2/tmp/tmp.qaam4Es89F/E---3.1_3191010.p',binunionEcases) ).
thf(binunion,axiom,
( binunion
= ( ^ [X1: $i,X3: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qaam4Es89F/E---3.1_3191010.p',binunion) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X1: $i,X3: $i] :
( ( in @ X1 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qaam4Es89F/E---3.1_3191010.p',uniqinunit) ).
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/sandbox2/tmp/tmp.qaam4Es89F/E---3.1_3191010.p',setunionE) ).
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/sandbox2/tmp/tmp.qaam4Es89F/E---3.1_3191010.p',setadjoinE) ).
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,plain,
( binunion
= ( ^ [Z0: $i,Z1: $i] : ( setunion @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[binunion]) ).
thf(c_0_7,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 @ ( setunion @ ( setadjoin @ X2 @ ( setadjoin @ X5 @ emptyset ) ) ) )
=> ( ( ( in @ X1 @ X2 )
=> X4 )
=> ( ( ( in @ X1 @ X5 )
=> X4 )
=> X4 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),uniqinunit]),setunionE]),setadjoinE]) ).
thf(c_0_8,negated_conjecture,
! [X30: $i,X31: $i,X32: $i,X33: $o,X34: $i,X35: $i,X36: $o,X38: $i,X39: $i] :
( ( ( in @ X32 @ X31 )
| X33
| ( X32 = X30 )
| ~ ( in @ X32 @ ( setadjoin @ X30 @ X31 ) ) )
& ( ~ X33
| X33
| ( X32 = X30 )
| ~ ( in @ X32 @ ( setadjoin @ X30 @ X31 ) ) )
& ( ( in @ X32 @ X31 )
| X33
| ~ X33
| ~ ( in @ X32 @ ( setadjoin @ X30 @ X31 ) ) )
& ( ~ X33
| X33
| ~ X33
| ~ ( in @ X32 @ ( setadjoin @ X30 @ X31 ) ) )
& ( ( in @ X35 @ ( esk1_3 @ X34 @ X35 @ X36 ) )
| X36
| ~ ( in @ X35 @ ( setunion @ X34 ) ) )
& ( ( in @ ( esk1_3 @ X34 @ X35 @ X36 ) @ X34 )
| X36
| ~ ( in @ X35 @ ( setunion @ X34 ) ) )
& ( ~ X36
| X36
| ~ ( in @ X35 @ ( setunion @ X34 ) ) )
& ( ~ ( in @ X38 @ ( setadjoin @ X39 @ emptyset ) )
| ( X38 = X39 ) )
& ( in @ esk4_0 @ ( setunion @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) ) )
& ( ~ ( 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_7])])])])])]) ).
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_8])])]) ).
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_8])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,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_13,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 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
in @ esk4_0 @ ( setunion @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
( epred1_0
| ~ ( in @ esk4_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_16,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,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_8])])]) ).
thf(c_0_18,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_13,c_0_14]) ).
thf(c_0_19,negated_conjecture,
~ ( in @ esk4_0 @ esk3_0 ),
inference(sr,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
( epred1_0
| ~ ( in @ esk4_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_21,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(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14])]),c_0_19]) ).
thf(c_0_22,negated_conjecture,
~ ( in @ esk4_0 @ esk2_0 ),
inference(sr,[status(thm)],[c_0_20,c_0_16]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_14])]),c_0_22]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n008.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 13:53:24 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.qaam4Es89F/E---3.1_3191010.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.07/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.07/0.26 % ehoh_best_sine_rwall with pid 3191024 completed with status 0
% 0.07/0.26 % Result found by ehoh_best_sine_rwall
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGUSF-FFSF32-MSFFMFNN
% 0.07/0.26 % partial match(1): HGUSF-FFSF32-MHFFMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 3191028 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGUSF-FFSF32-MSFFMFNN
% 0.07/0.26 % partial match(1): HGUSF-FFSF32-MHFFMFNN
% 0.07/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 13
% 0.07/0.26 % Removed by relevancy pruning/SinE : 8
% 0.07/0.26 % Initial clauses : 12
% 0.07/0.26 % Removed in clause preprocessing : 4
% 0.07/0.26 % Initial clauses in saturation : 8
% 0.07/0.26 % Processed clauses : 61
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 61
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 1
% 0.07/0.26 % Generated clauses : 247
% 0.07/0.26 % ...of the previous two non-redundant : 246
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 246
% 0.07/0.26 % Factorizations : 1
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 6
% 0.07/0.26 % ...of those cached : 4
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 60
% 0.07/0.26 % Positive orientable unit clauses : 2
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 3
% 0.07/0.26 % Non-unit-clauses : 55
% 0.07/0.26 % Current number of unprocessed clauses: 192
% 0.07/0.26 % ...number of literals in the above : 582
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 1
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 810
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 804
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 1
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 1
% 0.07/0.26 % BW rewrite match successes : 1
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 8740
% 0.07/0.26 % Search garbage collected termcells : 451
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.010 s
% 0.07/0.26 % System time : 0.001 s
% 0.07/0.26 % Total time : 0.011 s
% 0.07/0.26 % Maximum resident set size: 3640 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.013 s
% 0.07/0.26 % System time : 0.004 s
% 0.07/0.26 % Total time : 0.017 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------