%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU697^2 : 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 : n008.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 08:25:15 AM UTC 2026
% Result : Theorem 0.11s 0.27s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 24 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 87 ( 5 ~; 1 |; 1 &; 74 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 33 ( 20 ^; 13 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_25,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(decl_26,type,
esk1_0: $i ).
thf(decl_27,type,
esk2_0: $i ).
thf(decl_28,type,
esk3_0: $i > $i ).
thf(lam2lamEq,conjecture,
! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ( ( lam @ X1 @ X2
@ ^ [X4: $i] : ( X3 @ X4 ) )
= ( lam @ X1 @ X2
@ ^ [X4: $i] : ( X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QOwPjxLwsE/E---3.1_3218425.p',lam2lamEq) ).
thf(lam,axiom,
( lam
= ( ^ [X1: $i,X2: $i,X3: $i > $i] :
( dpsetconstr @ X1 @ X2
@ ^ [X4: $i,X5: $i] :
( ( X3 @ X4 )
= X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.QOwPjxLwsE/E---3.1_3218425.p',lam) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ( ( lam @ X1 @ X2
@ ^ [X4: $i] : ( X3 @ X4 ) )
= ( lam @ X1 @ X2
@ ^ [X4: $i] : ( X3 @ X4 ) ) ) ),
inference(assume_negation,[status(cth)],[lam2lamEq]) ).
thf(c_0_3,plain,
( lam
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i] :
( dpsetconstr @ Z0 @ Z1
@ ^ [Z3: $i,Z4: $i] :
( ( Z2 @ Z3 )
= Z4 ) ) ) ),
inference(fof_simplification,[status(thm)],[lam]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i,X2: $i,X3: $i > $i] :
( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( in @ ( X3 @ X4 ) @ X2 ) )
=> ( ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X3 @ Z0 ) ) )
= ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i] : ( $eq @ ( X3 @ Z0 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2]),c_0_3])]) ).
thf(c_0_5,negated_conjecture,
! [X13: $i] :
( ( ~ ( in @ X13 @ esk1_0 )
| ( in @ ( esk3_0 @ X13 ) @ esk2_0 ) )
& ( ( dpsetconstr @ esk1_0 @ esk2_0
@ ^ [Z0: $i] : ( $eq @ ( esk3_0 @ Z0 ) ) )
!= ( dpsetconstr @ esk1_0 @ esk2_0
@ ^ [Z0: $i] : ( $eq @ ( esk3_0 @ Z0 ) ) ) ) ),
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_4])])])])]) ).
thf(c_0_6,negated_conjecture,
( ( dpsetconstr @ esk1_0 @ esk2_0
@ ^ [Z0: $i] : ( $eq @ ( esk3_0 @ Z0 ) ) )
!= ( dpsetconstr @ esk1_0 @ esk2_0
@ ^ [Z0: $i] : ( $eq @ ( esk3_0 @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
$false,
inference(cn,[status(thm)],[c_0_6]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU697^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n008.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 14:12:24 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.24 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.QOwPjxLwsE/E---3.1_3218425.p
% 0.11/0.27 % Version: 3.5.1-ho
% 0.11/0.27 % partial match(1): HSSSSMSSSSMNSSN
% 0.11/0.27 % Preprocessing class: HSSSSMSSSSMNHSN.
% 0.11/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.27 % Starting sh3 with 1500s (5) cores
% 0.11/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.11/0.27 % Starting sh2lt with 300s (1) cores
% 0.11/0.27 % Starting ho_unfolding_1 with 300s (1) cores
% 0.11/0.27 % ehoh_best8_lambda with pid 3218461 completed with status 0
% 0.11/0.27 % Result found by ehoh_best8_lambda
% 0.11/0.27 % partial match(1): HSSSSMSSSSMNSSN
% 0.11/0.27 % Preprocessing class: HSSSSMSSSSMNHSN.
% 0.11/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.27 % Starting sh3 with 1500s (5) cores
% 0.11/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.11/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.11/0.27 % No SInE strategy applied
% 0.11/0.27 % Search class: HHHNF-FFSF00-SHSFFFNN
% 0.11/0.27 % partial match(1): HHHNF-FFSF00-SSSFFFNN
% 0.11/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.27 % SubtermCWHack with pid 3218464 completed with status 0
% 0.11/0.27 % Result found by SubtermCWHack
% 0.11/0.27 % partial match(1): HSSSSMSSSSMNSSN
% 0.11/0.27 % Preprocessing class: HSSSSMSSSSMNHSN.
% 0.11/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.27 % Starting sh3 with 1500s (5) cores
% 0.11/0.27 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.11/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.11/0.27 % No SInE strategy applied
% 0.11/0.27 % Search class: HHHNF-FFSF00-SHSFFFNN
% 0.11/0.27 % partial match(1): HHHNF-FFSF00-SSSFFFNN
% 0.11/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.11/0.27 % Preprocessing time : 0.002 s
% 0.11/0.27
% 0.11/0.27 % Proof found!
% 0.11/0.27 % SZS status Theorem
% 0.11/0.27 % SZS output start CNFRefutation
% See solution above
% 0.11/0.27 % Parsed axioms : 5
% 0.11/0.27 % Removed by relevancy pruning/SinE : 0
% 0.11/0.27 % Initial clauses : 5
% 0.11/0.27 % Removed in clause preprocessing : 3
% 0.11/0.27 % Initial clauses in saturation : 2
% 0.11/0.27 % Processed clauses : 1
% 0.11/0.27 % ...of these trivial : 0
% 0.11/0.27 % ...subsumed : 0
% 0.11/0.27 % ...remaining for further processing : 0
% 0.11/0.27 % Other redundant clauses eliminated : 0
% 0.11/0.27 % Clauses deleted for lack of memory : 0
% 0.11/0.27 % Backward-subsumed : 0
% 0.11/0.27 % Backward-rewritten : 0
% 0.11/0.27 % Generated clauses : 0
% 0.11/0.27 % ...of the previous two non-redundant : 0
% 0.11/0.27 % ...aggressively subsumed : 0
% 0.11/0.27 % Contextual simplify-reflections : 0
% 0.11/0.27 % Paramodulations : 0
% 0.11/0.27 % Factorizations : 0
% 0.11/0.27 % NegExts : 0
% 0.11/0.27 % Equation resolutions : 0
% 0.11/0.27 % Disequality decompositions : 0
% 0.11/0.27 % Total rewrite steps : 0
% 0.11/0.27 % ...of those cached : 0
% 0.11/0.27 % Propositional unsat checks : 0
% 0.11/0.27 % Propositional check models : 0
% 0.11/0.27 % Propositional check unsatisfiable : 0
% 0.11/0.27 % Propositional clauses : 0
% 0.11/0.27 % Propositional clauses after purity: 0
% 0.11/0.27 % Propositional unsat core size : 0
% 0.11/0.27 % Propositional preprocessing time : 0.000
% 0.11/0.27 % Propositional encoding time : 0.000
% 0.11/0.27 % Propositional solver time : 0.000
% 0.11/0.27 % Success case prop preproc time : 0.000
% 0.11/0.27 % Success case prop encoding time : 0.000
% 0.11/0.27 % Success case prop solver time : 0.000
% 0.11/0.27 % Current number of processed clauses : 0
% 0.11/0.27 % Positive orientable unit clauses : 0
% 0.11/0.27 % Positive unorientable unit clauses: 0
% 0.11/0.27 % Negative unit clauses : 0
% 0.11/0.27 % Non-unit-clauses : 0
% 0.11/0.27 % Current number of unprocessed clauses: 1
% 0.11/0.27 % ...number of literals in the above : 2
% 0.11/0.27 % Current number of archived formulas : 0
% 0.11/0.27 % Current number of archived clauses : 0
% 0.11/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.27 % Non-unit clause-clause subsumptions : 0
% 0.11/0.27 % Unit Clause-clause subsumption calls : 0
% 0.11/0.27 % Rewrite failures with RHS unbound : 0
% 0.11/0.27 % BW rewrite match attempts : 0
% 0.11/0.27 % BW rewrite match successes : 0
% 0.11/0.27 % Condensation attempts : 0
% 0.11/0.27 % Condensation successes : 0
% 0.11/0.27 % Termbank termtop insertions : 329
% 0.11/0.27 % Search garbage collected termcells : 106
% 0.11/0.27
% 0.11/0.27 % -------------------------------------------------
% 0.11/0.27 % User time : 0.005 s
% 0.11/0.27 % System time : 0.001 s
% 0.11/0.27 % Total time : 0.006 s
% 0.11/0.27 % Maximum resident set size: 3888 pages
% 0.11/0.27
% 0.11/0.27 % -------------------------------------------------
% 0.11/0.27 % User time : 0.008 s
% 0.11/0.27 % System time : 0.007 s
% 0.11/0.27 % Total time : 0.015 s
% 0.11/0.27 % Maximum resident set size: 4864 pages
% 0.11/0.27 % E exiting
%------------------------------------------------------------------------------