%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU596^2 : 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 08:24:39 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 12 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 166 ( 18 ~; 11 |; 7 &; 109 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 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 : 46 ( 0 ^; 43 !; 3 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
emptyI: $o ).
thf(decl_26,type,
binintersect: $i > $i > $i ).
thf(decl_27,type,
binintersectEL: $o ).
thf(decl_28,type,
binintersectER: $o ).
thf(decl_29,type,
esk1_1: $i > $i ).
thf(decl_30,type,
esk2_0: $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(disjointsetsI1,conjecture,
( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X1: $i,X3: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X3 ) )
=> ( ( binintersect @ X1 @ X3 )
= emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4xrurBMJA1/E---3.1_4038831.p',disjointsetsI1) ).
thf(emptyI,axiom,
( emptyI
<=> ! [X1: $i] :
( ! [X2: $i] :
~ ( in @ X2 @ X1 )
=> ( X1 = emptyset ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4xrurBMJA1/E---3.1_4038831.p',emptyI) ).
thf(binintersectEL,axiom,
( binintersectEL
<=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X3 ) )
=> ( in @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4xrurBMJA1/E---3.1_4038831.p',binintersectEL) ).
thf(binintersectER,axiom,
( binintersectER
<=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X3 ) )
=> ( in @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.4xrurBMJA1/E---3.1_4038831.p',binintersectER) ).
thf(c_0_4,negated_conjecture,
~ ( emptyI
=> ( binintersectEL
=> ( binintersectER
=> ! [X1: $i,X3: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X3 ) )
=> ( ( binintersect @ X1 @ X3 )
= emptyset ) ) ) ) ),
inference(assume_negation,[status(cth)],[disjointsetsI1]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X15: $i] :
( ! [X16: $i] :
~ ( in @ X16 @ X15 )
=> ( X15 = emptyset ) )
=> ( ! [X17: $i,X18: $i,X19: $i] :
( ( in @ X19 @ ( binintersect @ X17 @ X18 ) )
=> ( in @ X19 @ X17 ) )
=> ( ! [X20: $i,X21: $i,X22: $i] :
( ( in @ X22 @ ( binintersect @ X20 @ X21 ) )
=> ( in @ X22 @ X21 ) )
=> ! [X1: $i,X3: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X1 )
& ( in @ X2 @ X3 ) )
=> ( ( binintersect @ X1 @ X3 )
= emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,emptyI]),binintersectEL]),binintersectER])]) ).
thf(c_0_6,negated_conjecture,
! [X23: $i,X25: $i,X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X33: $i] :
( ( ( in @ ( esk1_1 @ X23 ) @ X23 )
| ( X23 = emptyset ) )
& ( ~ ( in @ X27 @ ( binintersect @ X25 @ X26 ) )
| ( in @ X27 @ X25 ) )
& ( ~ ( in @ X30 @ ( binintersect @ X28 @ X29 ) )
| ( in @ X30 @ X29 ) )
& ( ~ ( in @ X33 @ esk2_0 )
| ~ ( in @ X33 @ esk3_0 ) )
& ( ( binintersect @ esk2_0 @ esk3_0 )
!= emptyset ) ),
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,X3: $i] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( binintersect @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i] :
( ( in @ ( esk1_1 @ X1 ) @ X1 )
| ( X1 = emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk2_0 )
| ~ ( in @ X1 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( binintersect @ X1 @ X2 )
= emptyset )
| ( in @ ( esk1_1 @ ( binintersect @ X1 @ X2 ) ) @ X2 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ X1 @ ( binintersect @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( ( binintersect @ X1 @ esk3_0 )
= emptyset )
| ~ ( in @ ( esk1_1 @ ( binintersect @ X1 @ esk3_0 ) ) @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( binintersect @ X1 @ X2 )
= emptyset )
| ( in @ ( esk1_1 @ ( binintersect @ X1 @ X2 ) ) @ X1 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
thf(c_0_14,negated_conjecture,
( ( binintersect @ esk2_0 @ esk3_0 )
!= emptyset ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU596^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:56:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.4xrurBMJA1/E---3.1_4038831.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.25 % post_as_ho3 with pid 4038863 completed with status 0
% 0.08/0.25 % Result found by post_as_ho3
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGHSF-FFSF21-SFFFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 4038866 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HGHSF-FFSF21-SFFFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 10
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 11
% 0.08/0.25 % Removed in clause preprocessing : 6
% 0.08/0.25 % Initial clauses in saturation : 5
% 0.08/0.25 % Processed clauses : 9
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 9
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 10
% 0.08/0.25 % ...of the previous two non-redundant : 9
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 10
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 0
% 0.08/0.25 % ...of those cached : 0
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 9
% 0.08/0.25 % Positive orientable unit clauses : 0
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 8
% 0.08/0.25 % Current number of unprocessed clauses: 5
% 0.08/0.25 % ...number of literals in the above : 10
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 0
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 13
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 11
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 849
% 0.08/0.25 % Search garbage collected termcells : 244
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.004 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.005 s
% 0.08/0.25 % Maximum resident set size: 3580 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.004 s
% 0.08/0.25 % Total time : 0.010 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------