%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU811^2 : 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 : n013.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 08:25:43 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 26 equ; 0 cnn)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 241 ( 27 ~; 24 |; 11 &; 136 @)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 2 ^; 50 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
omega: $i ).
thf(decl_26,type,
setadjoinIL: $o ).
thf(decl_27,type,
setadjoinE: $o ).
thf(decl_28,type,
in__Cong: $o ).
thf(decl_29,type,
notinself2: $o ).
thf(decl_30,type,
omegaS: $i > $i ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(peanoSinj,conjecture,
( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( omegaS @ X1 )
= ( omegaS @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WtTREdHZaa/E---3.1_2202384.p',peanoSinj) ).
thf(omegaS,axiom,
( omegaS
= ( ^ [X1: $i] : ( setadjoin @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WtTREdHZaa/E---3.1_2202384.p',omegaS) ).
thf(setadjoinE,axiom,
( setadjoinE
<=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
=> ! [X4: $o] :
( ( ( X2 = X1 )
=> X4 )
=> ( ( ( in @ X2 @ X3 )
=> X4 )
=> X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WtTREdHZaa/E---3.1_2202384.p',setadjoinE) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X3: $i,X5: $i] :
( ( X3 = X5 )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ X3 )
<=> ( in @ X2 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WtTREdHZaa/E---3.1_2202384.p',in__Cong) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WtTREdHZaa/E---3.1_2202384.p',setadjoinIL) ).
thf(notinself2,axiom,
( notinself2
<=> ! [X3: $i,X5: $i] :
( ( in @ X3 @ X5 )
=> ~ ( in @ X5 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WtTREdHZaa/E---3.1_2202384.p',notinself2) ).
thf(c_0_6,negated_conjecture,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( omegaS @ X1 )
= ( omegaS @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[peanoSinj]) ).
thf(c_0_7,plain,
( omegaS
= ( ^ [Z0: $i] : ( setadjoin @ Z0 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[omegaS]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X20: $i,X21: $i] : ( in @ X20 @ ( setadjoin @ X20 @ X21 ) )
=> ( ! [X22: $i,X23: $i,X24: $i] :
( ( in @ X24 @ ( setadjoin @ X22 @ X23 ) )
=> ! [X25: $o] :
( ( ( X24 = X22 )
=> X25 )
=> ( ( ( in @ X24 @ X23 )
=> X25 )
=> X25 ) ) )
=> ( ! [X26: $i,X27: $i] :
( ( X26 = X27 )
=> ! [X28: $i,X29: $i] :
( ( X28 = X29 )
=> ( ( in @ X28 @ X26 )
<=> ( in @ X29 @ X27 ) ) ) )
=> ( ! [X30: $i,X31: $i] :
( ( in @ X30 @ X31 )
=> ~ ( in @ X31 @ X30 ) )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ! [X2: $i] :
( ( in @ X2 @ omega )
=> ( ( ( setadjoin @ X1 @ X1 )
= ( setadjoin @ X2 @ X2 ) )
=> ( X1 = X2 ) ) ) ) ) ) ) ),
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,setadjoinE]),in__Cong]),setadjoinIL]),c_0_7]),notinself2])]) ).
thf(c_0_9,negated_conjecture,
! [X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $o,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i] :
( ( in @ X32 @ ( setadjoin @ X32 @ X33 ) )
& ( ( 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 @ X40 @ X38 )
| ( in @ X41 @ X39 )
| ( X40 != X41 )
| ( X38 != X39 ) )
& ( ~ ( in @ X41 @ X39 )
| ( in @ X40 @ X38 )
| ( X40 != X41 )
| ( X38 != X39 ) )
& ( ~ ( in @ X42 @ X43 )
| ~ ( in @ X43 @ X42 ) )
& ( in @ esk1_0 @ omega )
& ( in @ esk2_0 @ omega )
& ( ( setadjoin @ esk1_0 @ esk1_0 )
= ( setadjoin @ esk2_0 @ esk2_0 ) )
& ( esk1_0 != esk2_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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( setadjoin @ esk1_0 @ esk1_0 )
= ( setadjoin @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,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_9])])]) ).
thf(c_0_13,negated_conjecture,
in @ esk1_0 @ ( setadjoin @ esk2_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i,X1: $i] :
( ~ ( in @ X1 @ X2 )
| ~ ( in @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
in @ esk1_0 @ esk2_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( X1 = esk1_0 )
| ( in @ X1 @ esk1_0 )
| ~ ( in @ X1 @ ( setadjoin @ esk2_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
thf(c_0_18,negated_conjecture,
~ ( in @ esk2_0 @ esk1_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_14]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU811^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:32:51 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.WtTREdHZaa/E---3.1_2202384.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % Starting lpo1_def_fix with 300s (1) cores
% 0.07/0.25 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.07/0.25 % ehoh_best_sine_rwall with pid 2202398 completed with status 0
% 0.07/0.25 % Result found by ehoh_best_sine_rwall
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGHSF-FFSS22-SSFFMFNN
% 0.07/0.25 % partial match(1): HGHSF-FFSS21-SSFFMFNN
% 0.07/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 2202401 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGHSF-FFSS22-SSFFMFNN
% 0.07/0.25 % partial match(1): HGHSF-FFSS21-SSFFMFNN
% 0.07/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 14
% 0.07/0.25 % Removed by relevancy pruning/SinE : 8
% 0.07/0.25 % Initial clauses : 12
% 0.07/0.25 % Removed in clause preprocessing : 5
% 0.07/0.25 % Initial clauses in saturation : 7
% 0.07/0.25 % Processed clauses : 16
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 1
% 0.07/0.25 % ...remaining for further processing : 15
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 10
% 0.07/0.25 % ...of the previous two non-redundant : 9
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 10
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 0
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 15
% 0.07/0.25 % Positive orientable unit clauses : 6
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 6
% 0.07/0.25 % Non-unit-clauses : 3
% 0.07/0.25 % Current number of unprocessed clauses: 0
% 0.07/0.25 % ...number of literals in the above : 0
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 0
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 3
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 3
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 0.07/0.25 % Unit Clause-clause subsumption calls : 1
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 0
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 1262
% 0.07/0.25 % Search garbage collected termcells : 448
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.003 s
% 0.07/0.25 % Total time : 0.008 s
% 0.07/0.25 % Maximum resident set size: 3640 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.008 s
% 0.07/0.25 % Total time : 0.013 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------