%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU508^2 : 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 : n026.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 08:24:18 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 168 ( 13 ~; 10 |; 4 &; 116 @)
% ( 7 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 6 ^; 39 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrI: $o ).
thf(decl_26,type,
dsetconstrER: $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(decl_28,type,
epred1_0: $i > $o ).
thf(decl_29,type,
esk2_0: $i ).
thf(setbeta,conjecture,
( dsetconstrI
=> ( dsetconstrER
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
<=> ( X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wjkh3GT7vo/E---3.1_616892.p',setbeta) ).
thf(dsetconstrI,axiom,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wjkh3GT7vo/E---3.1_616892.p',dsetconstrI) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Wjkh3GT7vo/E---3.1_616892.p',dsetconstrER) ).
thf(c_0_3,negated_conjecture,
~ ( dsetconstrI
=> ( dsetconstrER
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
<=> ( X2 @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[setbeta]) ).
thf(c_0_4,plain,
( dsetconstrI
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrI]) ).
thf(c_0_5,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X14: $i,X15: $i > $o,X16: $i] :
( ( in @ X16 @ X14 )
=> ( ( X15 @ X16 )
=> ( in @ X16 @ ( dsetconstr @ X14 @ X15 ) ) ) )
=> ( ! [X17: $i,X18: $i > $o,X19: $i] :
( ( in @ X19 @ ( dsetconstr @ X17 @ X18 ) )
=> ( X18 @ X19 ) )
=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
<=> ( X2 @ X3 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4]),c_0_5])]) ).
thf(c_0_7,negated_conjecture,
! [X20: $i,X21: $i > $o,X22: $i,X23: $i,X24: $i > $o,X25: $i] :
( ( ~ ( in @ X22 @ X20 )
| ~ ( X21 @ X22 )
| ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) ) )
& ( ~ ( in @ X25 @ ( dsetconstr @ X23 @ X24 ) )
| ( X24 @ X25 ) )
& ( in @ esk2_0 @ esk1_0 )
& ( ~ ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) )
| ~ ( epred1_0 @ esk2_0 ) )
& ( ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) )
| ( epred1_0 @ esk2_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_6])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) )
| ( epred1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ~ ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) )
| ~ ( epred1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
epred1_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ( in @ esk2_0 @ ( dsetconstr @ esk1_0 @ epred1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_13,negated_conjecture,
! [X3: $i,X2: $i > $o,X1: $i] :
( ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
in @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU508^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n026.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 13:49:57 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.Wjkh3GT7vo/E---3.1_616892.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.09/0.25 % Starting new_bool_9 with 300s (1) cores
% 0.09/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.25 % new_ho_10 with pid 616920 completed with status 0
% 0.09/0.25 % Result found by new_ho_10
% 0.09/0.25 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HGHNF-FFSF22-SSSFMSBN
% 0.09/0.25 % partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.09/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.25 % Starting new_ho_10 with 901s (1) cores
% 0.09/0.25 % Starting new_bool_1 with 151s (1) cores
% 0.09/0.25 % Starting new_bool_2 with 151s (1) cores
% 0.09/0.25 % Starting new_bool_9 with 146s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 616925 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSLSSSLMNSSA.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HGHNF-FFSF22-SSSFMSBN
% 0.09/0.25 % partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.09/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 7
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 9
% 0.09/0.25 % Removed in clause preprocessing : 4
% 0.09/0.25 % Initial clauses in saturation : 5
% 0.09/0.25 % Processed clauses : 7
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 7
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 2
% 0.09/0.25 % Generated clauses : 4
% 0.09/0.25 % ...of the previous two non-redundant : 2
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 4
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 4
% 0.09/0.25 % ...of those cached : 2
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 5
% 0.09/0.25 % Positive orientable unit clauses : 2
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 2
% 0.09/0.25 % Current number of unprocessed clauses: 0
% 0.09/0.25 % ...number of literals in the above : 0
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 2
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 1
% 0.09/0.25 % BW rewrite match successes : 1
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 840
% 0.09/0.25 % Search garbage collected termcells : 298
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.003 s
% 0.09/0.25 % System time : 0.002 s
% 0.09/0.25 % Total time : 0.005 s
% 0.09/0.25 % Maximum resident set size: 3632 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.010 s
% 0.09/0.25 % System time : 0.011 s
% 0.09/0.25 % Total time : 0.021 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------