%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU634^2 : 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 : n006.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 08:24:49 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 5 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 206 ( 14 ~; 13 |; 7 &; 152 @)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 40 !; 2 ?; 42 :)
% 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,
uniqinunit: $o ).
thf(decl_28,type,
subset: $i > $i > $o ).
thf(decl_29,type,
subsetI2: $o ).
thf(decl_30,type,
setunionE2: $o ).
thf(decl_31,type,
esk1_2: $i > $i > $i ).
thf(decl_32,type,
esk2_2: $i > $i > $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(setunionsingleton1,conjecture,
( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [X3: $i] : ( subset @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.64a5ZO94zh/E---3.1_761273.p',setunionsingleton1) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.64a5ZO94zh/E---3.1_761273.p',uniqinunit) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X3: $i,X4: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( subset @ X3 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.64a5ZO94zh/E---3.1_761273.p',subsetI2) ).
thf(setunionE2,axiom,
( setunionE2
<=> ! [X3: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
=> ? [X5: $i] :
( ( in @ X5 @ X3 )
& ( in @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.64a5ZO94zh/E---3.1_761273.p',setunionE2) ).
thf(c_0_4,negated_conjecture,
~ ( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [X3: $i] : ( subset @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[setunionsingleton1]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X15: $i,X16: $i] :
( ( in @ X15 @ ( setadjoin @ X16 @ emptyset ) )
=> ( X15 = X16 ) )
=> ( ! [X17: $i,X18: $i] :
( ! [X19: $i] :
( ( in @ X19 @ X17 )
=> ( in @ X19 @ X18 ) )
=> ( subset @ X17 @ X18 ) )
=> ( ! [X20: $i,X21: $i] :
( ( in @ X21 @ ( setunion @ X20 ) )
=> ? [X22: $i] :
( ( in @ X22 @ X20 )
& ( in @ X21 @ X22 ) ) )
=> ! [X3: $i] : ( subset @ ( setunion @ ( setadjoin @ X3 @ emptyset ) ) @ X3 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,uniqinunit]),subsetI2]),setunionE2]) ).
thf(c_0_6,negated_conjecture,
! [X23: $i,X24: $i,X25: $i,X26: $i,X28: $i,X29: $i] :
( ( ~ ( in @ X23 @ ( setadjoin @ X24 @ emptyset ) )
| ( X23 = X24 ) )
& ( ( in @ ( esk1_2 @ X25 @ X26 ) @ X25 )
| ( subset @ X25 @ X26 ) )
& ( ~ ( in @ ( esk1_2 @ X25 @ X26 ) @ X26 )
| ( subset @ X25 @ X26 ) )
& ( ( in @ ( esk2_2 @ X28 @ X29 ) @ X28 )
| ~ ( in @ X29 @ ( setunion @ X28 ) ) )
& ( ( in @ X29 @ ( esk2_2 @ X28 @ X29 ) )
| ~ ( in @ X29 @ ( setunion @ X28 ) ) )
& ~ ( subset @ ( setunion @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk3_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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk2_2 @ X1 @ X2 ) @ X1 )
| ~ ( in @ X2 @ ( setunion @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( in @ X1 @ ( setunion @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( esk2_2 @ ( setadjoin @ X1 @ emptyset ) @ X2 )
= X1 )
| ~ ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ X1 @ X2 ) @ X1 )
| ( subset @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
| ~ ( in @ ( esk1_2 @ X1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk1_2 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) @ X1 )
| ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,negated_conjecture,
~ ( subset @ ( setunion @ ( setadjoin @ esk3_0 @ emptyset ) ) @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU634^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 14:00:09 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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.64a5ZO94zh/E---3.1_761273.p
% 0.09/0.26 % Version: 3.5.1-ho
% 0.09/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.26 % post_as_ho2 with pid 761289 completed with status 0
% 0.09/0.26 % Result found by post_as_ho2
% 0.09/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGUSF-FFSF21-SFFFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % SubtermCWHack with pid 761290 completed with status 0
% 0.09/0.26 % Result found by SubtermCWHack
% 0.09/0.26 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.09/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.26 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.09/0.26 % Starting post_as_ho8 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.26 % Starting post_as_ho2 with 300s (1) cores
% 0.09/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.26 % No SInE strategy applied
% 0.09/0.26 % Search class: HGUSF-FFSF21-SFFFMFNN
% 0.09/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.26 % Preprocessing time : 0.001 s
% 0.09/0.26
% 0.09/0.26 % Proof found!
% 0.09/0.26 % SZS status Theorem
% 0.09/0.26 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26 % Parsed axioms : 12
% 0.09/0.26 % Removed by relevancy pruning/SinE : 0
% 0.09/0.26 % Initial clauses : 14
% 0.09/0.26 % Removed in clause preprocessing : 8
% 0.09/0.26 % Initial clauses in saturation : 6
% 0.09/0.26 % Processed clauses : 21
% 0.09/0.26 % ...of these trivial : 0
% 0.09/0.26 % ...subsumed : 0
% 0.09/0.26 % ...remaining for further processing : 21
% 0.09/0.26 % Other redundant clauses eliminated : 0
% 0.09/0.26 % Clauses deleted for lack of memory : 0
% 0.09/0.26 % Backward-subsumed : 0
% 0.09/0.26 % Backward-rewritten : 1
% 0.09/0.26 % Generated clauses : 22
% 0.09/0.26 % ...of the previous two non-redundant : 22
% 0.09/0.26 % ...aggressively subsumed : 0
% 0.09/0.26 % Contextual simplify-reflections : 0
% 0.09/0.26 % Paramodulations : 22
% 0.09/0.26 % Factorizations : 0
% 0.09/0.26 % NegExts : 0
% 0.09/0.26 % Equation resolutions : 0
% 0.09/0.26 % Disequality decompositions : 0
% 0.09/0.26 % Total rewrite steps : 1
% 0.09/0.26 % ...of those cached : 0
% 0.09/0.26 % Propositional unsat checks : 0
% 0.09/0.26 % Propositional check models : 0
% 0.09/0.26 % Propositional check unsatisfiable : 0
% 0.09/0.26 % Propositional clauses : 0
% 0.09/0.26 % Propositional clauses after purity: 0
% 0.09/0.26 % Propositional unsat core size : 0
% 0.09/0.26 % Propositional preprocessing time : 0.000
% 0.09/0.26 % Propositional encoding time : 0.000
% 0.09/0.26 % Propositional solver time : 0.000
% 0.09/0.26 % Success case prop preproc time : 0.000
% 0.09/0.26 % Success case prop encoding time : 0.000
% 0.09/0.26 % Success case prop solver time : 0.000
% 0.09/0.26 % Current number of processed clauses : 20
% 0.09/0.26 % Positive orientable unit clauses : 3
% 0.09/0.26 % Positive unorientable unit clauses: 0
% 0.09/0.26 % Negative unit clauses : 0
% 0.09/0.26 % Non-unit-clauses : 17
% 0.09/0.26 % Current number of unprocessed clauses: 7
% 0.09/0.26 % ...number of literals in the above : 14
% 0.09/0.26 % Current number of archived formulas : 0
% 0.09/0.26 % Current number of archived clauses : 1
% 0.09/0.26 % Clause-clause subsumption calls (NU) : 51
% 0.09/0.26 % Rec. Clause-clause subsumption calls : 37
% 0.09/0.26 % Non-unit clause-clause subsumptions : 0
% 0.09/0.26 % Unit Clause-clause subsumption calls : 18
% 0.09/0.26 % Rewrite failures with RHS unbound : 0
% 0.09/0.26 % BW rewrite match attempts : 4
% 0.09/0.26 % BW rewrite match successes : 1
% 0.09/0.26 % Condensation attempts : 0
% 0.09/0.26 % Condensation successes : 0
% 0.09/0.26 % Termbank termtop insertions : 1233
% 0.09/0.26 % Search garbage collected termcells : 252
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.004 s
% 0.09/0.26 % System time : 0.001 s
% 0.09/0.26 % Total time : 0.005 s
% 0.09/0.26 % Maximum resident set size: 3636 pages
% 0.09/0.26
% 0.09/0.26 % -------------------------------------------------
% 0.09/0.26 % User time : 0.007 s
% 0.09/0.26 % System time : 0.004 s
% 0.09/0.26 % Total time : 0.011 s
% 0.09/0.26 % Maximum resident set size: 4864 pages
% 0.09/0.26 % E exiting
%------------------------------------------------------------------------------