%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU709^2 : 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 08:25:18 AM UTC 2026
% Result : Theorem 0.24s 0.28s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 16 equ; 0 cnn)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 338 ( 31 ~; 22 |; 11 &; 230 @)
% ( 7 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% 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,
setadjoinIL: $o ).
thf(decl_27,type,
in__Cong: $o ).
thf(decl_28,type,
secondinupair: $o ).
thf(decl_29,type,
if: $i > $o > $i > $i > $i ).
thf(decl_30,type,
iftrue: $o ).
thf(decl_31,type,
iffalse: $o ).
thf(decl_32,type,
esk1_0: $i ).
thf(decl_33,type,
epred1_0: $o ).
thf(decl_34,type,
esk2_0: $i ).
thf(decl_35,type,
esk3_0: $i ).
thf(iftrueorfalse,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X3: $i,X5: $o,X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( in @ ( if @ X3 @ X5 @ X1 @ X2 ) @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iH6K7C3vav/E---3.1_4066561.p',iftrueorfalse) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ X3 )
<=> ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iH6K7C3vav/E---3.1_4066561.p',in__Cong) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iH6K7C3vav/E---3.1_4066561.p',setadjoinIL) ).
thf(iftrue,axiom,
( iftrue
<=> ! [X3: $i,X5: $o,X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( X5
=> ( ( if @ X3 @ X5 @ X1 @ X2 )
= X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iH6K7C3vav/E---3.1_4066561.p',iftrue) ).
thf(iffalse,axiom,
( iffalse
<=> ! [X3: $i,X5: $o,X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ~ X5
=> ( ( if @ X3 @ X5 @ X1 @ X2 )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iH6K7C3vav/E---3.1_4066561.p',iffalse) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.iH6K7C3vav/E---3.1_4066561.p',secondinupair) ).
thf(c_0_6,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [X3: $i,X5: $o,X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( in @ ( if @ X3 @ X5 @ X1 @ X2 ) @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[iftrueorfalse]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X26: $i,X27: $i] : ( in @ X26 @ ( setadjoin @ X26 @ X27 ) )
=> ( ! [X28: $i,X29: $i] :
( ( X28 = X29 )
=> ! [X30: $i,X31: $i] :
( ( X30 = X31 )
=> ( ( in @ X30 @ X28 )
<=> ( in @ X31 @ X29 ) ) ) )
=> ( ! [X32: $i,X33: $i] : ( in @ X33 @ ( setadjoin @ X32 @ ( setadjoin @ X33 @ emptyset ) ) )
=> ( ! [X34: $i,X35: $o,X36: $i] :
( ( in @ X36 @ X34 )
=> ! [X37: $i] :
( ( in @ X37 @ X34 )
=> ( X35
=> ( ( if @ X34 @ X35 @ X36 @ X37 )
= X36 ) ) ) )
=> ( ! [X38: $i,X39: $o,X40: $i] :
( ( in @ X40 @ X38 )
=> ! [X41: $i] :
( ( in @ X41 @ X38 )
=> ( ~ X39
=> ( ( if @ X38 @ X39 @ X40 @ X41 )
= X41 ) ) ) )
=> ! [X3: $i,X5: $o,X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( in @ ( if @ X3 @ X5 @ X1 @ X2 ) @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ),
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,in__Cong]),setadjoinIL]),iftrue]),iffalse]),secondinupair])]) ).
thf(c_0_8,negated_conjecture,
! [X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i,X50: $i,X51: $o,X52: $i,X53: $i,X54: $i,X55: $o,X56: $i,X57: $i] :
( ( in @ X42 @ ( setadjoin @ X42 @ X43 ) )
& ( ~ ( in @ X46 @ X44 )
| ( in @ X47 @ X45 )
| ( X46 != X47 )
| ( X44 != X45 ) )
& ( ~ ( in @ X47 @ X45 )
| ( in @ X46 @ X44 )
| ( X46 != X47 )
| ( X44 != X45 ) )
& ( in @ X49 @ ( setadjoin @ X48 @ ( setadjoin @ X49 @ emptyset ) ) )
& ( ~ ( in @ X52 @ X50 )
| ~ ( in @ X53 @ X50 )
| ~ X51
| ( ( if @ X50 @ X51 @ X52 @ X53 )
= X52 ) )
& ( ~ ( in @ X56 @ X54 )
| ~ ( in @ X57 @ X54 )
| X55
| ( ( if @ X54 @ X55 @ X56 @ X57 )
= X57 ) )
& ( in @ esk2_0 @ esk1_0 )
& ( in @ esk3_0 @ esk1_0 )
& ( ~ epred1_0
| epred1_0 )
& ( ~ ( in @ ( if @ esk1_0 @ $false @ esk2_0 @ esk3_0 ) @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) )
| epred1_0 )
& ( ~ epred1_0
| ~ ( in @ ( if @ esk1_0 @ $true @ esk2_0 @ esk3_0 ) @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) ) )
& ( ~ ( in @ ( if @ esk1_0 @ $false @ esk2_0 @ esk3_0 ) @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) )
| ~ ( in @ ( if @ esk1_0 @ $true @ esk2_0 @ esk3_0 ) @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[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,
( ~ epred1_0
| ~ ( in @ ( if @ esk1_0 @ $true @ esk2_0 @ esk3_0 ) @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( if @ X2 @ $true @ X1 @ X3 )
= X1 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X2 ) ),
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] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
( epred1_0
| ~ ( in @ ( if @ esk1_0 @ ~ $true @ esk2_0 @ esk3_0 ) @ ( setadjoin @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( if @ X2 @ ~ $true @ X1 @ X3 )
= X3 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_8])])]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13])]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_12]),c_0_13])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU709^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:13:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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.iH6K7C3vav/E---3.1_4066561.p
% 0.24/0.28 % Version: 3.5.1-ho
% 0.24/0.28 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho8 with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho3 with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho2 with 300s (1) cores
% 0.24/0.28 % post_as_ho8 with pid 4066575 completed with status 0
% 0.24/0.28 % Result found by post_as_ho8
% 0.24/0.28 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho8 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.24/0.28 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.24/0.28 % Search class: HHHSS-FFSF33-SFFFMFNN
% 0.24/0.28 % partial match(3): HHUSF-FFSF32-SFFFMFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % SubtermCWHack with pid 4066578 completed with status 0
% 0.24/0.28 % Result found by SubtermCWHack
% 0.24/0.28 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho8 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.24/0.28 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.24/0.28 % Search class: HHHSS-FFSF33-SFFFMFNN
% 0.24/0.28 % partial match(3): HHUSF-FFSF32-SFFFMFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % Preprocessing time : 0.001 s
% 0.24/0.28
% 0.24/0.28 % Proof found!
% 0.24/0.28 % SZS status Theorem
% 0.24/0.28 % SZS output start CNFRefutation
% See solution above
% 0.24/0.28 % Parsed axioms : 15
% 0.24/0.28 % Removed by relevancy pruning/SinE : 9
% 0.24/0.28 % Initial clauses : 12
% 0.24/0.28 % Removed in clause preprocessing : 3
% 0.24/0.28 % Initial clauses in saturation : 9
% 0.24/0.28 % Processed clauses : 9
% 0.24/0.28 % ...of these trivial : 0
% 0.24/0.28 % ...subsumed : 0
% 0.24/0.28 % ...remaining for further processing : 9
% 0.24/0.28 % Other redundant clauses eliminated : 0
% 0.24/0.28 % Clauses deleted for lack of memory : 0
% 0.24/0.28 % Backward-subsumed : 1
% 0.24/0.28 % Backward-rewritten : 0
% 0.24/0.28 % Generated clauses : 2
% 0.24/0.28 % ...of the previous two non-redundant : 1
% 0.24/0.28 % ...aggressively subsumed : 0
% 0.24/0.28 % Contextual simplify-reflections : 0
% 0.24/0.28 % Paramodulations : 2
% 0.24/0.28 % Factorizations : 0
% 0.24/0.28 % NegExts : 0
% 0.24/0.28 % Equation resolutions : 0
% 0.24/0.28 % Disequality decompositions : 0
% 0.24/0.28 % Total rewrite steps : 6
% 0.24/0.28 % ...of those cached : 2
% 0.24/0.28 % Propositional unsat checks : 0
% 0.24/0.28 % Propositional check models : 0
% 0.24/0.28 % Propositional check unsatisfiable : 0
% 0.24/0.28 % Propositional clauses : 0
% 0.24/0.28 % Propositional clauses after purity: 0
% 0.24/0.28 % Propositional unsat core size : 0
% 0.24/0.28 % Propositional preprocessing time : 0.000
% 0.24/0.28 % Propositional encoding time : 0.000
% 0.24/0.28 % Propositional solver time : 0.000
% 0.24/0.28 % Success case prop preproc time : 0.000
% 0.24/0.28 % Success case prop encoding time : 0.000
% 0.24/0.28 % Success case prop solver time : 0.000
% 0.24/0.28 % Current number of processed clauses : 8
% 0.24/0.28 % Positive orientable unit clauses : 4
% 0.24/0.28 % Positive unorientable unit clauses: 0
% 0.24/0.28 % Negative unit clauses : 1
% 0.24/0.28 % Non-unit-clauses : 3
% 0.24/0.28 % Current number of unprocessed clauses: 1
% 0.24/0.28 % ...number of literals in the above : 2
% 0.24/0.28 % Current number of archived formulas : 0
% 0.24/0.28 % Current number of archived clauses : 1
% 0.24/0.28 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.28 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.28 % Non-unit clause-clause subsumptions : 0
% 0.24/0.28 % Unit Clause-clause subsumption calls : 3
% 0.24/0.28 % Rewrite failures with RHS unbound : 0
% 0.24/0.28 % BW rewrite match attempts : 0
% 0.24/0.28 % BW rewrite match successes : 0
% 0.24/0.28 % Condensation attempts : 0
% 0.24/0.28 % Condensation successes : 0
% 0.24/0.28 % Termbank termtop insertions : 1525
% 0.24/0.28 % Search garbage collected termcells : 581
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.004 s
% 0.24/0.28 % System time : 0.003 s
% 0.24/0.28 % Total time : 0.007 s
% 0.24/0.28 % Maximum resident set size: 3844 pages
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.006 s
% 0.24/0.28 % System time : 0.008 s
% 0.24/0.28 % Total time : 0.014 s
% 0.24/0.28 % Maximum resident set size: 4864 pages
% 0.24/0.28 % E exiting
%------------------------------------------------------------------------------