%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU805^2 : 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 08:25:42 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 26 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 216 ( 29 ~; 17 |; 15 &; 133 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 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 : 52 ( 2 ^; 36 !; 14 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
foundationAx: $o ).
thf(decl_26,type,
nonempty: $i > $o ).
thf(decl_27,type,
nonemptyE1: $o ).
thf(decl_28,type,
binintersect: $i > $i > $i ).
thf(decl_29,type,
disjointsetsI1: $o ).
thf(decl_30,type,
esk1_1: $i > $i ).
thf(decl_31,type,
esk2_1: $i > $i ).
thf(decl_32,type,
esk3_2: $i > $i > $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(nonempty,axiom,
( nonempty
= ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.d520m8ebof/E---3.1_164746.p',nonempty) ).
thf(foundation2,conjecture,
( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X1: $i] :
( ( nonempty @ X1 )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( binintersect @ X4 @ X1 )
= emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.d520m8ebof/E---3.1_164746.p',foundation2) ).
thf(nonemptyE1,axiom,
( nonemptyE1
<=> ! [X1: $i] :
( ( nonempty @ X1 )
=> ? [X2: $i] : ( in @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.d520m8ebof/E---3.1_164746.p',nonemptyE1) ).
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/sandbox2/tmp/tmp.d520m8ebof/E---3.1_164746.p',foundationAx) ).
thf(disjointsetsI1,axiom,
( disjointsetsI1
<=> ! [X1: $i,X3: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X3 ) )
=> ( ( binintersect @ X1 @ X3 )
= emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.d520m8ebof/E---3.1_164746.p',disjointsetsI1) ).
thf(c_0_5,plain,
( nonempty
= ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
inference(fof_simplification,[status(thm)],[nonempty]) ).
thf(c_0_6,negated_conjecture,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [X1: $i] :
( ( nonempty @ X1 )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( binintersect @ X4 @ X1 )
= emptyset ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[foundation2]) ).
thf(c_0_7,axiom,
( nonemptyE1
= ( ! [X1: $i] :
( ( X1 != emptyset )
=> ? [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(apply_def,[status(thm)],[nonemptyE1,c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X16: $i] :
( ? [X17: $i] : ( in @ X17 @ X16 )
=> ? [X18: $i] :
( ( in @ X18 @ X16 )
& ~ ? [X19: $i] :
( ( in @ X19 @ X18 )
& ( in @ X19 @ X16 ) ) ) )
=> ( ! [X20: $i] :
( ( X20 != emptyset )
=> ? [X21: $i] : ( in @ X21 @ X20 ) )
=> ( ! [X22: $i,X23: $i] :
( ~ ? [X24: $i] :
( ( in @ X24 @ X22 )
& ( in @ X24 @ X23 ) )
=> ( ( binintersect @ X22 @ X23 )
= emptyset ) )
=> ! [X1: $i] :
( ( X1 != emptyset )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( binintersect @ X4 @ X1 )
= 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)],[c_0_6,foundationAx]),c_0_5]),c_0_7]),disjointsetsI1])]) ).
thf(c_0_9,negated_conjecture,
! [X25: $i,X26: $i,X28: $i,X29: $i,X31: $i,X32: $i,X35: $i] :
( ( ( in @ ( esk1_1 @ X25 ) @ X25 )
| ~ ( in @ X26 @ X25 ) )
& ( ~ ( in @ X28 @ ( esk1_1 @ X25 ) )
| ~ ( in @ X28 @ X25 )
| ~ ( in @ X26 @ X25 ) )
& ( ( X29 = emptyset )
| ( in @ ( esk2_1 @ X29 ) @ X29 ) )
& ( ( in @ ( esk3_2 @ X31 @ X32 ) @ X31 )
| ( ( binintersect @ X31 @ X32 )
= emptyset ) )
& ( ( in @ ( esk3_2 @ X31 @ X32 ) @ X32 )
| ( ( binintersect @ X31 @ X32 )
= emptyset ) )
& ( esk4_0 != emptyset )
& ( ~ ( in @ X35 @ esk4_0 )
| ( ( binintersect @ X35 @ esk4_0 )
!= emptyset ) ) ),
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,X3: $i,X2: $i] :
( ~ ( in @ X1 @ ( esk1_1 @ X2 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( esk1_1 @ X2 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(condense,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk3_2 @ X1 @ X2 ) @ X1 )
| ( ( binintersect @ X1 @ X2 )
= emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( binintersect @ ( esk1_1 @ X1 ) @ X2 )
= emptyset )
| ~ ( in @ ( esk3_2 @ ( esk1_1 @ X1 ) @ X2 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( esk3_2 @ X1 @ X2 ) @ X2 )
| ( ( binintersect @ X1 @ X2 )
= emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk4_0 )
| ( ( binintersect @ X1 @ esk4_0 )
!= emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( binintersect @ ( esk1_1 @ X1 ) @ X1 )
= emptyset ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i,X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ X1 )
| ~ ( in @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
( ( X1 = emptyset )
| ( in @ ( esk2_1 @ X1 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_19,negated_conjecture,
~ ( in @ ( esk1_1 @ esk4_0 ) @ esk4_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ( X1 = emptyset )
| ( in @ ( esk1_1 @ X1 ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
esk4_0 != emptyset,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU805^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:34:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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.d520m8ebof/E---3.1_164746.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.22/0.27 % Starting lpo1_def_fix with 300s (1) cores
% 0.22/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.22/0.27 % new_ho_10 with pid 164776 completed with status 0
% 0.22/0.27 % Result found by new_ho_10
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHSF-FFSF21-SSFFMFNN
% 0.22/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.27 % Starting sh5l with 151s (1) cores
% 0.22/0.27 % Starting new_bool_1 with 151s (1) cores
% 0.22/0.27 % Starting new_bool_2 with 146s (1) cores
% 0.22/0.27 % sh5l with pid 164783 completed with status 0
% 0.22/0.27 % Result found by sh5l
% 0.22/0.27 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHSF-FFSF21-SSFFMFNN
% 0.22/0.27 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.27 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.27 % Starting sh5l with 151s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27 % Presaturation interreduction done
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 12
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 14
% 0.22/0.27 % Removed in clause preprocessing : 7
% 0.22/0.27 % Initial clauses in saturation : 7
% 0.22/0.27 % Processed clauses : 26
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 2
% 0.22/0.27 % ...remaining for further processing : 24
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 0
% 0.22/0.27 % Generated clauses : 16
% 0.22/0.27 % ...of the previous two non-redundant : 15
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 16
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 0
% 0.22/0.27 % ...of those cached : 0
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 17
% 0.22/0.27 % Positive orientable unit clauses : 2
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 2
% 0.22/0.27 % Non-unit-clauses : 13
% 0.22/0.27 % Current number of unprocessed clauses: 2
% 0.22/0.27 % ...number of literals in the above : 4
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 7
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 30
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 28
% 0.22/0.27 % Non-unit clause-clause subsumptions : 3
% 0.22/0.27 % Unit Clause-clause subsumption calls : 7
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 2
% 0.22/0.27 % BW rewrite match successes : 0
% 0.22/0.27 % Condensation attempts : 26
% 0.22/0.27 % Condensation successes : 1
% 0.22/0.27 % Termbank termtop insertions : 1465
% 0.22/0.27 % Search garbage collected termcells : 322
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.004 s
% 0.22/0.27 % System time : 0.001 s
% 0.22/0.27 % Total time : 0.005 s
% 0.22/0.27 % Maximum resident set size: 3832 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.015 s
% 0.22/0.27 % System time : 0.011 s
% 0.22/0.27 % Total time : 0.027 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------