%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV447^1 : 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 08:39:45 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 74 ( 4 ~; 0 |; 0 &; 70 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 5 ^; 17 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
nil: $i ).
thf(decl_24,type,
cons: $i > $i > $i ).
thf(decl_25,type,
map: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
esk1_0: $i ).
thf(test,conjecture,
! [X4: $i] :
( ( map
@ ^ [X2: $i] : X2
@ ( cons @ X4 @ nil ) )
= ( cons @ X4 @ nil ) ),
file('/export/starexec/sandbox2/tmp/tmp.6b4JHy7Goa/E---3.1_4185531.p',test) ).
thf(ax2,axiom,
! [X1: $i > $i,X2: $i,X3: $i] :
( ( map @ X1 @ ( cons @ X2 @ X3 ) )
= ( cons @ ( X1 @ X2 ) @ ( map @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6b4JHy7Goa/E---3.1_4185531.p',ax2) ).
thf(ax1,axiom,
! [X1: $i > $i] :
( ( map @ X1 @ nil )
= nil ),
file('/export/starexec/sandbox2/tmp/tmp.6b4JHy7Goa/E---3.1_4185531.p',ax1) ).
thf(c_0_3,negated_conjecture,
~ ! [X4: $i] :
( ( map
@ ^ [X2: $i] : X2
@ ( cons @ X4 @ nil ) )
= ( cons @ X4 @ nil ) ),
inference(assume_negation,[status(cth)],[test]) ).
thf(c_0_4,negated_conjecture,
~ ! [X4: $i] :
( ( map
@ ^ [Z0: $i] : Z0
@ ( cons @ X4 @ nil ) )
= ( cons @ X4 @ nil ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X11: $i > $i,X12: $i,X13: $i] :
( ( map @ X11 @ ( cons @ X12 @ X13 ) )
= ( cons @ ( X11 @ X12 ) @ ( map @ X11 @ X13 ) ) ),
inference(variable_rename,[status(thm)],[ax2]) ).
thf(c_0_6,plain,
! [X10: $i > $i] :
( ( map @ X10 @ nil )
= nil ),
inference(variable_rename,[status(thm)],[ax1]) ).
thf(c_0_7,negated_conjecture,
( ( map
@ ^ [Z0: $i] : Z0
@ ( cons @ esk1_0 @ nil ) )
!= ( cons @ esk1_0 @ nil ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
thf(c_0_8,plain,
! [X1: $i > $i,X2: $i,X3: $i] :
( ( map @ X1 @ ( cons @ X2 @ X3 ) )
= ( cons @ ( X1 @ X2 ) @ ( map @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X1: $i > $i] :
( ( map @ X1 @ nil )
= nil ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( map
@ ^ [Z0: $i] : Z0
@ ( cons @ esk1_0 @ nil ) )
!= ( cons @ esk1_0 @ nil ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X1: $i > $i,X2: $i] :
( ( map @ X1 @ ( cons @ X2 @ nil ) )
= ( cons @ ( X1 @ X2 ) @ nil ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV447^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % 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 16:04:45 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.6b4JHy7Goa/E---3.1_4185531.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.25 % Starting new_bool_9 with 300s (1) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % post_as_ho10 with pid 4185545 completed with status 0
% 0.08/0.25 % Result found by post_as_ho10
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HUUPS-FFSF22-SSSFFFNN
% 0.08/0.25 % partial match(2): HUUPS-FFSF22-SFFFFFNN
% 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 4185548 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSSSNSSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HUUPS-FFSF22-SSSFFFNN
% 0.08/0.25 % partial match(2): HUUPS-FFSF22-SFFFFFNN
% 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 : 6
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 6
% 0.08/0.25 % Removed in clause preprocessing : 3
% 0.08/0.25 % Initial clauses in saturation : 3
% 0.08/0.25 % Processed clauses : 4
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 4
% 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 : 6
% 0.08/0.25 % ...of the previous two non-redundant : 4
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 6
% 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 : 4
% 0.08/0.25 % Positive orientable unit clauses : 3
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 0
% 0.08/0.25 % Current number of unprocessed clauses: 2
% 0.08/0.25 % ...number of literals in the above : 2
% 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) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 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 : 1
% 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 : 322
% 0.08/0.25 % Search garbage collected termcells : 30
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.003 s
% 0.08/0.25 % System time : 0.001 s
% 0.08/0.25 % Total time : 0.004 s
% 0.08/0.25 % Maximum resident set size: 3632 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.005 s
% 0.08/0.25 % System time : 0.005 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
%------------------------------------------------------------------------------