%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU636^2 : 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 : n018.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 08:27:01 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 8 ~; 4 |; 3 &; 74 @)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
setunion: $i > $i ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
setextsub: $o ).
thf(decl_28,type,
setunionsingleton1: $o ).
thf(decl_29,type,
setunionsingleton2: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(setunionsingleton,conjecture,
( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X3: $i] :
( ( setunion @ ( setadjoin @ X3 @ emptyset ) )
= X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nO1i0q60nn/E---3.1_121829.p',setunionsingleton) ).
thf(setextsub,axiom,
( setextsub
<=> ! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X2 @ X1 )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nO1i0q60nn/E---3.1_121829.p',setextsub) ).
thf(setunionsingleton1,axiom,
( setunionsingleton1
<=> ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.nO1i0q60nn/E---3.1_121829.p',setunionsingleton1) ).
thf(setunionsingleton2,axiom,
( setunionsingleton2
<=> ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nO1i0q60nn/E---3.1_121829.p',setunionsingleton2) ).
thf(c_0_4,negated_conjecture,
~ ( setextsub
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ! [X3: $i] :
( ( setunion @ ( setadjoin @ X3 @ emptyset ) )
= X3 ) ) ) ),
inference(assume_negation,[status(cth)],[setunionsingleton]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X9: $i,X10: $i] :
( ( subset @ X9 @ X10 )
=> ( ( subset @ X10 @ X9 )
=> ( X9 = X10 ) ) )
=> ( ! [X11: $i] : ( subset @ ( setunion @ ( setadjoin @ X11 @ emptyset ) ) @ X11 )
=> ( ! [X12: $i] : ( subset @ X12 @ ( setunion @ ( setadjoin @ X12 @ emptyset ) ) )
=> ! [X3: $i] :
( ( setunion @ ( setadjoin @ X3 @ emptyset ) )
= X3 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,setextsub]),setunionsingleton1]),setunionsingleton2]) ).
thf(c_0_6,negated_conjecture,
! [X13: $i,X14: $i,X15: $i,X16: $i] :
( ( ~ ( subset @ X13 @ X14 )
| ~ ( subset @ X14 @ X13 )
| ( X13 = X14 ) )
& ( subset @ ( setunion @ ( setadjoin @ X15 @ emptyset ) ) @ X15 )
& ( subset @ X16 @ ( setunion @ ( setadjoin @ X16 @ emptyset ) ) )
& ( ( setunion @ ( setadjoin @ esk1_0 @ emptyset ) )
!= esk1_0 ) ),
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_5])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( subset @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( setunion @ ( setadjoin @ esk1_0 @ emptyset ) )
!= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU636^2 : 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 : n018.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 14:03:11 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 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.nO1i0q60nn/E---3.1_121829.p
% 0.23/0.27 % Version: 3.5.1-ho
% 0.23/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.27 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.27 % post_as_ho8 with pid 121843 completed with status 0
% 0.23/0.27 % Result found by post_as_ho8
% 0.23/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.23/0.27 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.23/0.27 % Search class: HHUSS-FFSF21-SFFFMFNN
% 0.23/0.27 % partial match(2): FHUSS-FFSF21-SFFFFFNN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % SubtermCWHack with pid 121851 completed with status 0
% 0.23/0.27 % Result found by SubtermCWHack
% 0.23/0.27 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.27 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.23/0.27 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.23/0.27 % Search class: HHUSS-FFSF21-SFFFMFNN
% 0.23/0.27 % partial match(2): FHUSS-FFSF21-SFFFFFNN
% 0.23/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.27 % Preprocessing time : 0.001 s
% 0.23/0.27
% 0.23/0.27 % Proof found!
% 0.23/0.27 % SZS status Theorem
% 0.23/0.27 % SZS output start CNFRefutation
% See solution above
% 0.23/0.27 % Parsed axioms : 11
% 0.23/0.27 % Removed by relevancy pruning/SinE : 7
% 0.23/0.27 % Initial clauses : 4
% 0.23/0.27 % Removed in clause preprocessing : 0
% 0.23/0.27 % Initial clauses in saturation : 4
% 0.23/0.27 % Processed clauses : 5
% 0.23/0.27 % ...of these trivial : 0
% 0.23/0.27 % ...subsumed : 0
% 0.23/0.27 % ...remaining for further processing : 5
% 0.23/0.27 % Other redundant clauses eliminated : 0
% 0.23/0.27 % Clauses deleted for lack of memory : 0
% 0.23/0.27 % Backward-subsumed : 0
% 0.23/0.27 % Backward-rewritten : 3
% 0.23/0.27 % Generated clauses : 2
% 0.23/0.27 % ...of the previous two non-redundant : 4
% 0.23/0.27 % ...aggressively subsumed : 0
% 0.23/0.27 % Contextual simplify-reflections : 0
% 0.23/0.27 % Paramodulations : 2
% 0.23/0.27 % Factorizations : 0
% 0.23/0.27 % NegExts : 0
% 0.23/0.27 % Equation resolutions : 0
% 0.23/0.27 % Disequality decompositions : 0
% 0.23/0.27 % Total rewrite steps : 5
% 0.23/0.27 % ...of those cached : 1
% 0.23/0.27 % Propositional unsat checks : 0
% 0.23/0.27 % Propositional check models : 0
% 0.23/0.27 % Propositional check unsatisfiable : 0
% 0.23/0.27 % Propositional clauses : 0
% 0.23/0.27 % Propositional clauses after purity: 0
% 0.23/0.27 % Propositional unsat core size : 0
% 0.23/0.27 % Propositional preprocessing time : 0.000
% 0.23/0.27 % Propositional encoding time : 0.000
% 0.23/0.27 % Propositional solver time : 0.000
% 0.23/0.27 % Success case prop preproc time : 0.000
% 0.23/0.27 % Success case prop encoding time : 0.000
% 0.23/0.27 % Success case prop solver time : 0.000
% 0.23/0.27 % Current number of processed clauses : 2
% 0.23/0.27 % Positive orientable unit clauses : 1
% 0.23/0.27 % Positive unorientable unit clauses: 0
% 0.23/0.27 % Negative unit clauses : 0
% 0.23/0.27 % Non-unit-clauses : 1
% 0.23/0.27 % Current number of unprocessed clauses: 1
% 0.23/0.27 % ...number of literals in the above : 1
% 0.23/0.27 % Current number of archived formulas : 0
% 0.23/0.27 % Current number of archived clauses : 3
% 0.23/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.27 % Non-unit clause-clause subsumptions : 0
% 0.23/0.27 % Unit Clause-clause subsumption calls : 0
% 0.23/0.27 % Rewrite failures with RHS unbound : 0
% 0.23/0.27 % BW rewrite match attempts : 2
% 0.23/0.27 % BW rewrite match successes : 2
% 0.23/0.27 % Condensation attempts : 0
% 0.23/0.27 % Condensation successes : 0
% 0.23/0.27 % Termbank termtop insertions : 472
% 0.23/0.27 % Search garbage collected termcells : 142
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.005 s
% 0.23/0.27 % System time : 0.000 s
% 0.23/0.27 % Total time : 0.005 s
% 0.23/0.27 % Maximum resident set size: 3632 pages
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.006 s
% 0.23/0.27 % System time : 0.005 s
% 0.23/0.27 % Total time : 0.011 s
% 0.23/0.27 % Maximum resident set size: 4864 pages
% 0.23/0.27 % E exiting
%------------------------------------------------------------------------------