%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU806^2 : 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 08:25:42 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 13 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 208 ( 29 ~; 17 |; 10 &; 126 @)
% ( 6 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 50 !; 6 ?; 56 :)
% 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,
foundationAx: $o ).
thf(decl_27,type,
setadjoinIL: $o ).
thf(decl_28,type,
uniqinunit: $o ).
thf(decl_29,type,
in__Cong: $o ).
thf(decl_30,type,
esk1_1: $i > $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(notinself,conjecture,
( foundationAx
=> ( setadjoinIL
=> ( uniqinunit
=> ( in__Cong
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.66IuPy5q35/E---3.1_807882.p',notinself) ).
thf(setadjoinIL,axiom,
( setadjoinIL
<=> ! [X2: $i,X4: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.66IuPy5q35/E---3.1_807882.p',setadjoinIL) ).
thf(foundationAx,axiom,
( foundationAx
<=> ! [X1: $i] :
( ? [X2: $i] : ( in @ X2 @ X1 )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ~ ? [X2: $i] :
( ( in @ X2 @ X3 )
& ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.66IuPy5q35/E---3.1_807882.p',foundationAx) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X2: $i,X4: $i] :
( ( in @ X2 @ ( setadjoin @ X4 @ emptyset ) )
=> ( X2 = X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.66IuPy5q35/E---3.1_807882.p',uniqinunit) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X1: $i,X3: $i] :
( ( X1 = X3 )
=> ! [X2: $i,X4: $i] :
( ( X2 = X4 )
=> ( ( in @ X2 @ X1 )
<=> ( in @ X4 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.66IuPy5q35/E---3.1_807882.p',in__Cong) ).
thf(c_0_5,negated_conjecture,
~ ( foundationAx
=> ( setadjoinIL
=> ( uniqinunit
=> ( in__Cong
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[notinself]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X18: $i] :
( ? [X19: $i] : ( in @ X19 @ X18 )
=> ? [X20: $i] :
( ( in @ X20 @ X18 )
& ~ ? [X21: $i] :
( ( in @ X21 @ X20 )
& ( in @ X21 @ X18 ) ) ) )
=> ( ! [X22: $i,X23: $i] : ( in @ X22 @ ( setadjoin @ X22 @ X23 ) )
=> ( ! [X24: $i,X25: $i] :
( ( in @ X24 @ ( setadjoin @ X25 @ emptyset ) )
=> ( X24 = X25 ) )
=> ( ! [X26: $i,X27: $i] :
( ( X26 = X27 )
=> ! [X28: $i,X29: $i] :
( ( X28 = X29 )
=> ( ( in @ X28 @ X26 )
<=> ( in @ X29 @ X27 ) ) ) )
=> ! [X1: $i] :
~ ( in @ X1 @ X1 ) ) ) ) ),
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)],[c_0_5,setadjoinIL]),foundationAx]),uniqinunit]),in__Cong])]) ).
thf(c_0_7,negated_conjecture,
! [X30: $i,X31: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X38: $i,X39: $i,X40: $i,X41: $i] :
( ( ( in @ ( esk1_1 @ X30 ) @ X30 )
| ~ ( in @ X31 @ X30 ) )
& ( ~ ( in @ X33 @ ( esk1_1 @ X30 ) )
| ~ ( in @ X33 @ X30 )
| ~ ( in @ X31 @ X30 ) )
& ( in @ X34 @ ( setadjoin @ X34 @ X35 ) )
& ( ~ ( in @ X36 @ ( setadjoin @ X37 @ emptyset ) )
| ( X36 = X37 ) )
& ( ~ ( in @ X40 @ X38 )
| ( in @ X41 @ X39 )
| ( X40 != X41 )
| ( X38 != X39 ) )
& ( ~ ( in @ X41 @ X39 )
| ( in @ X40 @ X38 )
| ( X40 != X41 )
| ( X38 != X39 ) )
& ( in @ esk2_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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ X1 )
| ~ ( in @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk1_1 @ ( setadjoin @ X1 @ X2 ) ) @ ( setadjoin @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ~ ( in @ X1 @ ( esk1_1 @ X2 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] :
( ( esk1_1 @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
thf(c_0_16,negated_conjecture,
in @ esk2_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
~ ( in @ X1 @ X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_11]),c_0_13]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_16,c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU806^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n006.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 14:32:24 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.66IuPy5q35/E---3.1_807882.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.07/0.25 % post_as_ho8 with pid 807896 completed with status 0
% 0.07/0.25 % Result found by post_as_ho8
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.07/0.25 % Search class: HHHSF-FFSF21-SFFFMFNN
% 0.07/0.25 % partial match(1): HGHSF-FFSF21-SFFFMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 807904 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.07/0.25 % Search class: HHHSF-FFSF21-SFFFMFNN
% 0.07/0.25 % partial match(1): HGHSF-FFSF21-SFFFMFNN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (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 : 12
% 0.07/0.25 % Removed by relevancy pruning/SinE : 7
% 0.07/0.25 % Initial clauses : 7
% 0.07/0.25 % Removed in clause preprocessing : 2
% 0.07/0.25 % Initial clauses in saturation : 5
% 0.07/0.25 % Processed clauses : 11
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 11
% 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 : 1
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 12
% 0.07/0.25 % ...of the previous two non-redundant : 8
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 11
% 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 : 4
% 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 : 9
% 0.07/0.25 % Positive orientable unit clauses : 4
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 4
% 0.07/0.25 % Current number of unprocessed clauses: 1
% 0.07/0.25 % ...number of literals in the above : 1
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 2
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 6
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 6
% 0.07/0.25 % Non-unit clause-clause subsumptions : 1
% 0.07/0.25 % Unit Clause-clause subsumption calls : 4
% 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 : 1062
% 0.07/0.25 % Search garbage collected termcells : 355
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.002 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3636 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.006 s
% 0.07/0.25 % System time : 0.007 s
% 0.07/0.25 % Total time : 0.012 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------