%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP100^1 : TPTP v9.3.1. Released v7.5.0.
% 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 08:05:31 AM UTC 2026
% Result : Theorem 0.25s 0.39s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 108 ( 4 ~; 0 |; 0 &; 104 @)
% ( 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 : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 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/sandbox2/tmp/tmp.R3RcUQ6t27/E---3.1_1100192.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/sandbox2/tmp/tmp.R3RcUQ6t27/E---3.1_1100192.p',fact_151_i__append__assoc) ).
thf(fact_160_append__Cons,axiom,
! [X467: a,X468: list_a,X469: list_a] :
( ( append_a @ ( cons_a @ X467 @ X468 ) @ X469 )
= ( cons_a @ X467 @ ( append_a @ X468 @ X469 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.R3RcUQ6t27/E---3.1_1100192.p',fact_160_append__Cons) ).
thf(fact_164_append_Oleft__neutral,axiom,
! [X268: list_a] :
( ( append_a @ nil_a @ X268 )
= X268 ),
file('/export/starexec/sandbox2/tmp/tmp.R3RcUQ6t27/E---3.1_1100192.p',fact_164_append_Oleft__neutral) ).
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(assume_negation,[status(cth)],[conj_0]) ).
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_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,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_5]) ).
thf(c_0_7,plain,
! [X1570: list_a,X1571: list_a,X1572: nat > a] :
( ( listIn1312259492pend_a @ X1570 @ ( listIn1312259492pend_a @ X1571 @ X1572 ) )
= ( listIn1312259492pend_a @ ( append_a @ X1570 @ X1571 ) @ X1572 ) ),
inference(variable_rename,[status(thm)],[fact_151_i__append__assoc]) ).
thf(c_0_8,plain,
! [X1724: a,X1725: list_a,X1726: list_a] :
( ( append_a @ ( cons_a @ X1724 @ X1725 ) @ X1726 )
= ( cons_a @ X1724 @ ( append_a @ X1725 @ X1726 ) ) ),
inference(variable_rename,[status(thm)],[fact_160_append__Cons]) ).
thf(c_0_9,plain,
! [X1780: list_a] :
( ( append_a @ nil_a @ X1780 )
= X1780 ),
inference(variable_rename,[status(thm)],[fact_164_append_Oleft__neutral]) ).
thf(c_0_10,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_6]) ).
thf(c_0_11,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_7]) ).
thf(c_0_12,plain,
! [X3: list_a,X7: a,X5: list_a] :
( ( append_a @ ( cons_a @ X7 @ X3 ) @ X5 )
= ( cons_a @ X7 @ ( append_a @ X3 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X3: list_a] :
( ( append_a @ nil_a @ X3 )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP100^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n026.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 19:56:12 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.22/0.27 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.R3RcUQ6t27/E---3.1_1100192.p
% 0.25/0.39 % Version: 3.5.1-ho
% 0.25/0.39 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.25/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.39 % Starting sh1 with 1500s (5) cores
% 0.25/0.39 % Starting new_ho_8 with 300s (1) cores
% 0.25/0.39 % Starting new_ho_11 with 300s (1) cores
% 0.25/0.39 % Starting sh5l with 300s (1) cores
% 0.25/0.39 % sh5l with pid 1100209 completed with status 0
% 0.25/0.39 % Result found by sh5l
% 0.25/0.39 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.25/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.39 % Starting sh1 with 1500s (5) cores
% 0.25/0.39 % Starting new_ho_8 with 300s (1) cores
% 0.25/0.39 % Starting new_ho_11 with 300s (1) cores
% 0.25/0.39 % Starting sh5l with 300s (1) cores
% 0.25/0.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.25/0.39 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.25/0.39 % Search class: HGHSM-FSLM31-DHSFFSBN
% 0.25/0.39 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.39 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.39 % SubtermCWHack with pid 1100211 completed with status 0
% 0.25/0.39 % Result found by SubtermCWHack
% 0.25/0.39 % Preprocessing class: HSLSSMSSSSMNHSA.
% 0.25/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.39 % Starting sh1 with 1500s (5) cores
% 0.25/0.39 % Starting new_ho_8 with 300s (1) cores
% 0.25/0.39 % Starting new_ho_11 with 300s (1) cores
% 0.25/0.39 % Starting sh5l with 300s (1) cores
% 0.25/0.39 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.25/0.39 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.25/0.39 % Search class: HGHSM-FSLM31-DHSFFSBN
% 0.25/0.39 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.39 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.39 % Preprocessing time : 0.005 s
% 0.25/0.39
% 0.25/0.39 % Proof found!
% 0.25/0.39 % SZS status Theorem
% 0.25/0.39 % SZS output start CNFRefutation
% See solution above
% 0.25/0.39 % Parsed axioms : 450
% 0.25/0.39 % Removed by relevancy pruning/SinE : 240
% 0.25/0.39 % Initial clauses : 540
% 0.25/0.39 % Removed in clause preprocessing : 41
% 0.25/0.39 % Initial clauses in saturation : 499
% 0.25/0.39 % Processed clauses : 1276
% 0.25/0.39 % ...of these trivial : 39
% 0.25/0.39 % ...subsumed : 633
% 0.25/0.39 % ...remaining for further processing : 603
% 0.25/0.39 % Other redundant clauses eliminated : 277
% 0.25/0.39 % Clauses deleted for lack of memory : 0
% 0.25/0.39 % Backward-subsumed : 7
% 0.25/0.39 % Backward-rewritten : 1
% 0.25/0.39 % Generated clauses : 3499
% 0.25/0.39 % ...of the previous two non-redundant : 2434
% 0.25/0.39 % ...aggressively subsumed : 0
% 0.25/0.39 % Contextual simplify-reflections : 0
% 0.25/0.39 % Paramodulations : 3220
% 0.25/0.39 % Factorizations : 12
% 0.25/0.39 % NegExts : 0
% 0.25/0.39 % Equation resolutions : 291
% 0.25/0.39 % Disequality decompositions : 0
% 0.25/0.39 % Total rewrite steps : 1486
% 0.25/0.39 % ...of those cached : 1203
% 0.25/0.39 % Propositional unsat checks : 0
% 0.25/0.39 % Propositional check models : 0
% 0.25/0.39 % Propositional check unsatisfiable : 0
% 0.25/0.39 % Propositional clauses : 0
% 0.25/0.39 % Propositional clauses after purity: 0
% 0.25/0.39 % Propositional unsat core size : 0
% 0.25/0.39 % Propositional preprocessing time : 0.000
% 0.25/0.39 % Propositional encoding time : 0.000
% 0.25/0.39 % Propositional solver time : 0.000
% 0.25/0.39 % Success case prop preproc time : 0.000
% 0.25/0.39 % Success case prop encoding time : 0.000
% 0.25/0.39 % Success case prop solver time : 0.000
% 0.25/0.39 % Current number of processed clauses : 510
% 0.25/0.39 % Positive orientable unit clauses : 124
% 0.25/0.39 % Positive unorientable unit clauses: 0
% 0.25/0.39 % Negative unit clauses : 29
% 0.25/0.39 % Non-unit-clauses : 357
% 0.25/0.39 % Current number of unprocessed clauses: 1603
% 0.25/0.39 % ...number of literals in the above : 4522
% 0.25/0.39 % Current number of archived formulas : 0
% 0.25/0.39 % Current number of archived clauses : 8
% 0.25/0.39 % Clause-clause subsumption calls (NU) : 44120
% 0.25/0.39 % Rec. Clause-clause subsumption calls : 29861
% 0.25/0.39 % Non-unit clause-clause subsumptions : 553
% 0.25/0.39 % Unit Clause-clause subsumption calls : 797
% 0.25/0.39 % Rewrite failures with RHS unbound : 0
% 0.25/0.39 % BW rewrite match attempts : 14
% 0.25/0.39 % BW rewrite match successes : 8
% 0.25/0.39 % Condensation attempts : 0
% 0.25/0.39 % Condensation successes : 0
% 0.25/0.39 % Termbank termtop insertions : 67781
% 0.25/0.39 % Search garbage collected termcells : 13821
% 0.25/0.39
% 0.25/0.39 % -------------------------------------------------
% 0.25/0.39 % User time : 0.065 s
% 0.25/0.39 % System time : 0.008 s
% 0.25/0.39 % Total time : 0.073 s
% 0.25/0.39 % Maximum resident set size: 6588 pages
% 0.25/0.39
% 0.25/0.39 % -------------------------------------------------
% 0.25/0.39 % User time : 0.081 s
% 0.25/0.39 % System time : 0.015 s
% 0.25/0.39 % Total time : 0.096 s
% 0.25/0.39 % Maximum resident set size: 5888 pages
% 0.25/0.39 % E exiting
%------------------------------------------------------------------------------