%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP100^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:04:21 AM UTC 2026
% Result : Theorem 0.44s 0.41s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 11 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 96 ( 4 ~; 0 |; 0 &; 92 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 0 ^; 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
list_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
nat: $tType ).
thf(decl_32,type,
listIn1312259492pend_a: list_a > ( nat > a ) > nat > a ).
thf(decl_36,type,
append_a: list_a > list_a > list_a ).
thf(decl_56,type,
cons_a: a > list_a > list_a ).
thf(decl_60,type,
nil_a: list_a ).
thf(decl_105,type,
f: nat > a ).
thf(decl_106,type,
x: a ).
thf(decl_107,type,
xs: list_a ).
thf(conj_0,conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LPFPeS2ERW/E---3.1_3841637.p',conj_0) ).
thf(fact_151_i__append__assoc,axiom,
! [X441: list_a,X442: list_a,X443: nat > a] :
( ( listIn1312259492pend_a @ X441 @ ( listIn1312259492pend_a @ X442 @ X443 ) )
= ( listIn1312259492pend_a @ ( append_a @ X441 @ X442 ) @ X443 ) ),
file('/export/starexec/sandbox/tmp/tmp.LPFPeS2ERW/E---3.1_3841637.p',fact_151_i__append__assoc) ).
thf(fact_186_append__eq__Cons,axiom,
! [X511: a,X512: list_a] :
( ( append_a @ ( cons_a @ X511 @ nil_a ) @ X512 )
= ( cons_a @ X511 @ X512 ) ),
file('/export/starexec/sandbox/tmp/tmp.LPFPeS2ERW/E---3.1_3841637.p',fact_186_append__eq__Cons) ).
thf(c_0_3,negated_conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
!= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_4,negated_conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
!= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
!= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X2750: list_a,X2751: list_a,X2752: nat > a] :
( ( listIn1312259492pend_a @ X2750 @ ( listIn1312259492pend_a @ X2751 @ X2752 ) )
= ( listIn1312259492pend_a @ ( append_a @ X2750 @ X2751 ) @ X2752 ) ),
inference(variable_rename,[status(thm)],[fact_151_i__append__assoc]) ).
thf(c_0_7,plain,
! [X2903: a,X2904: list_a] :
( ( append_a @ ( cons_a @ X2903 @ nil_a ) @ X2904 )
= ( cons_a @ X2903 @ X2904 ) ),
inference(variable_rename,[status(thm)],[fact_186_append__eq__Cons]) ).
thf(c_0_8,negated_conjecture,
( ( listIn1312259492pend_a @ ( cons_a @ x @ xs ) @ f )
!= ( listIn1312259492pend_a @ ( cons_a @ x @ nil_a ) @ ( listIn1312259492pend_a @ xs @ f ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X5: list_a,X3: list_a,X2: nat > a] :
( ( listIn1312259492pend_a @ X3 @ ( listIn1312259492pend_a @ X5 @ X2 ) )
= ( listIn1312259492pend_a @ ( append_a @ X3 @ X5 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X7: a,X3: list_a] :
( ( append_a @ ( cons_a @ X7 @ nil_a ) @ X3 )
= ( cons_a @ X7 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP100^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n007.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 19:51:26 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.LPFPeS2ERW/E---3.1_3841637.p
% 0.44/0.41 % Version: 3.5.1-ho
% 0.44/0.41 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.44/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.41 % Starting sh1 with 1500s (5) cores
% 0.44/0.41 % Starting new_ho_8 with 300s (1) cores
% 0.44/0.41 % Starting new_ho_11 with 300s (1) cores
% 0.44/0.41 % Starting sh5l with 300s (1) cores
% 0.44/0.41 % sh1 with pid 3841650 completed with status 0
% 0.44/0.41 % Result found by sh1
% 0.44/0.41 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.44/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.41 % Starting sh1 with 1500s (5) cores
% 0.44/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.44/0.41 % No SInE strategy applied
% 0.44/0.41 % Search class: HGHSM-SSLM32-MHSFFSBN
% 0.44/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.44/0.41 % Starting sh1 with 151s (1) cores
% 0.44/0.41 % Starting additional_ho_4 with 361s (1) cores
% 0.44/0.41 % Starting additional_ho_6 with 136s (1) cores
% 0.44/0.41 % Starting full_lambda_4 with 136s (1) cores
% 0.44/0.41 % additional_ho_6 with pid 3841660 completed with status 0
% 0.44/0.41 % Result found by additional_ho_6
% 0.44/0.41 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.44/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.44/0.41 % Starting sh1 with 1500s (5) cores
% 0.44/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.44/0.41 % No SInE strategy applied
% 0.44/0.41 % Search class: HGHSM-SSLM32-MHSFFSBN
% 0.44/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.44/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.44/0.41 % Starting sh1 with 151s (1) cores
% 0.44/0.41 % Starting additional_ho_4 with 361s (1) cores
% 0.44/0.41 % Starting additional_ho_6 with 136s (1) cores
% 0.44/0.41 % Preprocessing time : 0.019 s
% 0.44/0.41 % Presaturation interreduction done
% 0.44/0.41
% 0.44/0.41 % Proof found!
% 0.44/0.41 % SZS status Theorem
% 0.44/0.41 % SZS output start CNFRefutation
% See solution above
% 0.44/0.41 % Parsed axioms : 450
% 0.44/0.41 % Removed by relevancy pruning/SinE : 0
% 0.44/0.41 % Initial clauses : 1212
% 0.44/0.41 % Removed in clause preprocessing : 162
% 0.44/0.41 % Initial clauses in saturation : 1050
% 0.44/0.41 % Processed clauses : 278
% 0.44/0.41 % ...of these trivial : 8
% 0.44/0.41 % ...subsumed : 27
% 0.44/0.41 % ...remaining for further processing : 243
% 0.44/0.41 % Other redundant clauses eliminated : 90
% 0.44/0.41 % Clauses deleted for lack of memory : 0
% 0.44/0.41 % Backward-subsumed : 0
% 0.44/0.41 % Backward-rewritten : 2
% 0.44/0.41 % Generated clauses : 71
% 0.44/0.41 % ...of the previous two non-redundant : 26
% 0.44/0.41 % ...aggressively subsumed : 0
% 0.44/0.41 % Contextual simplify-reflections : 0
% 0.44/0.41 % Paramodulations : 0
% 0.44/0.41 % Factorizations : 0
% 0.44/0.41 % NegExts : 0
% 0.44/0.41 % Equation resolutions : 90
% 0.44/0.41 % Disequality decompositions : 0
% 0.44/0.41 % Total rewrite steps : 62
% 0.44/0.41 % ...of those cached : 25
% 0.44/0.41 % Propositional unsat checks : 0
% 0.44/0.41 % Propositional check models : 0
% 0.44/0.41 % Propositional check unsatisfiable : 0
% 0.44/0.41 % Propositional clauses : 0
% 0.44/0.41 % Propositional clauses after purity: 0
% 0.44/0.41 % Propositional unsat core size : 0
% 0.44/0.41 % Propositional preprocessing time : 0.000
% 0.44/0.41 % Propositional encoding time : 0.000
% 0.44/0.41 % Propositional solver time : 0.000
% 0.44/0.41 % Success case prop preproc time : 0.000
% 0.44/0.41 % Success case prop encoding time : 0.000
% 0.44/0.41 % Success case prop solver time : 0.000
% 0.44/0.41 % Current number of processed clauses : 170
% 0.44/0.41 % Positive orientable unit clauses : 77
% 0.44/0.41 % Positive unorientable unit clauses: 0
% 0.44/0.41 % Negative unit clauses : 16
% 0.44/0.41 % Non-unit-clauses : 77
% 0.44/0.41 % Current number of unprocessed clauses: 798
% 0.44/0.41 % ...number of literals in the above : 2872
% 0.44/0.41 % Current number of archived formulas : 0
% 0.44/0.41 % Current number of archived clauses : 2
% 0.44/0.41 % Clause-clause subsumption calls (NU) : 1196
% 0.44/0.41 % Rec. Clause-clause subsumption calls : 1008
% 0.44/0.41 % Non-unit clause-clause subsumptions : 23
% 0.44/0.41 % Unit Clause-clause subsumption calls : 134
% 0.44/0.41 % Rewrite failures with RHS unbound : 0
% 0.44/0.41 % BW rewrite match attempts : 4
% 0.44/0.41 % BW rewrite match successes : 2
% 0.44/0.41 % Condensation attempts : 0
% 0.44/0.41 % Condensation successes : 0
% 0.44/0.41 % Termbank termtop insertions : 77448
% 0.44/0.41 % Search garbage collected termcells : 23094
% 0.44/0.41
% 0.44/0.41 % -------------------------------------------------
% 0.44/0.41 % User time : 0.085 s
% 0.44/0.41 % System time : 0.019 s
% 0.44/0.41 % Total time : 0.104 s
% 0.44/0.41 % Maximum resident set size: 8636 pages
% 0.44/0.41
% 0.44/0.41 % -------------------------------------------------
% 0.44/0.41 % User time : 0.190 s
% 0.44/0.41 % System time : 0.061 s
% 0.44/0.41 % Total time : 0.252 s
% 0.44/0.41 % Maximum resident set size: 5888 pages
% 0.44/0.41 % E exiting
%------------------------------------------------------------------------------