%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP043^1 : 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 : 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 08:04:11 AM UTC 2026
% Result : Theorem 0.22s 0.35s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% 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 : 115 ( 5 ~; 0 |; 0 &; 110 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
list_a: $tType ).
thf(decl_sort2,type,
nat: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_24,type,
descar1375166517sums_a: list_a > list_a ).
thf(decl_30,type,
zero_zero_a: a ).
thf(decl_32,type,
append_a: list_a > list_a > list_a ).
thf(decl_38,type,
cons_a: a > list_a > list_a ).
thf(decl_44,type,
nth_a: list_a > nat > a ).
thf(decl_46,type,
replicate_a: nat > a > list_a ).
thf(decl_56,type,
p: nat ).
thf(decl_60,type,
xs1: list_a ).
thf(decl_61,type,
xs2: list_a ).
thf(decl_62,type,
xsa: list_a ).
thf(conj_0,conjecture,
( ( descar1375166517sums_a @ xsa )
= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.esJsBSpUEw/E---3.1_1088888.p',conj_0) ).
thf(fact_8_psums__replicate__0__append,axiom,
! [X3: nat,X4: list_a] :
( ( descar1375166517sums_a @ ( append_a @ ( replicate_a @ X3 @ zero_zero_a ) @ X4 ) )
= ( append_a @ ( replicate_a @ X3 @ zero_zero_a ) @ ( descar1375166517sums_a @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.esJsBSpUEw/E---3.1_1088888.p',fact_8_psums__replicate__0__append) ).
thf(fact_5_xs1__def,axiom,
( xs1
= ( replicate_a @ p @ zero_zero_a ) ),
file('/export/starexec/sandbox/tmp/tmp.esJsBSpUEw/E---3.1_1088888.p',fact_5_xs1__def) ).
thf(fact_6_xs__decompose,axiom,
( xsa
= ( append_a @ xs1 @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.esJsBSpUEw/E---3.1_1088888.p',fact_6_xs__decompose) ).
thf(c_0_4,negated_conjecture,
( ( descar1375166517sums_a @ xsa )
!= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
( ( descar1375166517sums_a @ xsa )
!= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X1696: nat,X1697: list_a] :
( ( descar1375166517sums_a @ ( append_a @ ( replicate_a @ X1696 @ zero_zero_a ) @ X1697 ) )
= ( append_a @ ( replicate_a @ X1696 @ zero_zero_a ) @ ( descar1375166517sums_a @ X1697 ) ) ),
inference(variable_rename,[status(thm)],[fact_8_psums__replicate__0__append]) ).
thf(c_0_7,negated_conjecture,
( ( descar1375166517sums_a @ xsa )
!= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X3: nat,X2: list_a] :
( ( descar1375166517sums_a @ ( append_a @ ( replicate_a @ X3 @ zero_zero_a ) @ X2 ) )
= ( append_a @ ( replicate_a @ X3 @ zero_zero_a ) @ ( descar1375166517sums_a @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
( xs1
= ( replicate_a @ p @ zero_zero_a ) ),
inference(split_conjunct,[status(thm)],[fact_5_xs1__def]) ).
thf(c_0_10,negated_conjecture,
( ( descar1375166517sums_a @ xsa )
!= ( append_a @ ( replicate_a @ p @ zero_zero_a ) @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X2: list_a] :
( ( descar1375166517sums_a @ ( append_a @ xs1 @ X2 ) )
= ( append_a @ xs1 @ ( descar1375166517sums_a @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,plain,
( xsa
= ( append_a @ xs1 @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) ),
inference(split_conjunct,[status(thm)],[fact_6_xs__decompose]) ).
thf(c_0_13,negated_conjecture,
( ( append_a @ xs1 @ ( descar1375166517sums_a @ ( cons_a @ ( nth_a @ xsa @ p ) @ xs2 ) ) )
!= ( descar1375166517sums_a @ xsa ) ),
inference(rw,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_14,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP043^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n026.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:43:27 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.25 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.esJsBSpUEw/E---3.1_1088888.p
% 0.22/0.35 % Version: 3.5.1-ho
% 0.22/0.35 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.22/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.35 % Starting new_ho_10_cnf2 with 300s (1) cores
% 0.22/0.35 % Starting full_lambda_6 with 300s (1) cores
% 0.22/0.35 % Starting full_lambda_9 with 300s (1) cores
% 0.22/0.35 % new_ho_10 with pid 1088919 completed with status 0
% 0.22/0.35 % Result found by new_ho_10
% 0.22/0.35 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.22/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.35 % No SInE strategy applied
% 0.22/0.35 % Search class: HGHSM-FSLM31-MHFFFSBN
% 0.22/0.35 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.35 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.35 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.35 % Starting pre_casc_8 with 151s (1) cores
% 0.22/0.35 % Starting additional_ho_6 with 151s (1) cores
% 0.22/0.35 % Starting full_lambda_10 with 146s (1) cores
% 0.22/0.35 % additional_ho_6 with pid 1088926 completed with status 0
% 0.22/0.35 % Result found by additional_ho_6
% 0.22/0.35 % Preprocessing class: HSLSSMSMSSSNHFA.
% 0.22/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.35 % No SInE strategy applied
% 0.22/0.35 % Search class: HGHSM-FSLM31-MHFFFSBN
% 0.22/0.35 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.35 % Starting SubtermCWHack with 151s (1) cores
% 0.22/0.35 % Starting new_ho_10 with 901s (1) cores
% 0.22/0.35 % Starting pre_casc_8 with 151s (1) cores
% 0.22/0.35 % Starting additional_ho_6 with 151s (1) cores
% 0.22/0.35 % Preprocessing time : 0.006 s
% 0.22/0.35 % Presaturation interreduction done
% 0.22/0.35
% 0.22/0.35 % Proof found!
% 0.22/0.35 % SZS status Theorem
% 0.22/0.35 % SZS output start CNFRefutation
% See solution above
% 0.22/0.35 % Parsed axioms : 399
% 0.22/0.35 % Removed by relevancy pruning/SinE : 0
% 0.22/0.35 % Initial clauses : 635
% 0.22/0.35 % Removed in clause preprocessing : 72
% 0.22/0.35 % Initial clauses in saturation : 563
% 0.22/0.35 % Processed clauses : 721
% 0.22/0.35 % ...of these trivial : 24
% 0.22/0.35 % ...subsumed : 98
% 0.22/0.35 % ...remaining for further processing : 599
% 0.22/0.35 % Other redundant clauses eliminated : 156
% 0.22/0.35 % Clauses deleted for lack of memory : 0
% 0.22/0.35 % Backward-subsumed : 0
% 0.22/0.35 % Backward-rewritten : 5
% 0.22/0.35 % Generated clauses : 260
% 0.22/0.35 % ...of the previous two non-redundant : 92
% 0.22/0.35 % ...aggressively subsumed : 0
% 0.22/0.35 % Contextual simplify-reflections : 2
% 0.22/0.35 % Paramodulations : 133
% 0.22/0.35 % Factorizations : 0
% 0.22/0.35 % NegExts : 0
% 0.22/0.35 % Equation resolutions : 156
% 0.22/0.35 % Disequality decompositions : 0
% 0.22/0.35 % Total rewrite steps : 436
% 0.22/0.35 % ...of those cached : 385
% 0.22/0.35 % Propositional unsat checks : 0
% 0.22/0.35 % Propositional check models : 0
% 0.22/0.35 % Propositional check unsatisfiable : 0
% 0.22/0.35 % Propositional clauses : 0
% 0.22/0.35 % Propositional clauses after purity: 0
% 0.22/0.35 % Propositional unsat core size : 0
% 0.22/0.35 % Propositional preprocessing time : 0.000
% 0.22/0.35 % Propositional encoding time : 0.000
% 0.22/0.35 % Propositional solver time : 0.000
% 0.22/0.35 % Success case prop preproc time : 0.000
% 0.22/0.35 % Success case prop encoding time : 0.000
% 0.22/0.35 % Success case prop solver time : 0.000
% 0.22/0.35 % Current number of processed clauses : 124
% 0.22/0.35 % Positive orientable unit clauses : 43
% 0.22/0.35 % Positive unorientable unit clauses: 0
% 0.22/0.35 % Negative unit clauses : 19
% 0.22/0.35 % Non-unit-clauses : 62
% 0.22/0.35 % Current number of unprocessed clauses: 304
% 0.22/0.35 % ...number of literals in the above : 789
% 0.22/0.35 % Current number of archived formulas : 0
% 0.22/0.35 % Current number of archived clauses : 376
% 0.22/0.35 % Clause-clause subsumption calls (NU) : 22941
% 0.22/0.35 % Rec. Clause-clause subsumption calls : 9410
% 0.22/0.35 % Non-unit clause-clause subsumptions : 84
% 0.22/0.35 % Unit Clause-clause subsumption calls : 209
% 0.22/0.35 % Rewrite failures with RHS unbound : 0
% 0.22/0.35 % BW rewrite match attempts : 20
% 0.22/0.35 % BW rewrite match successes : 16
% 0.22/0.35 % Condensation attempts : 0
% 0.22/0.35 % Condensation successes : 0
% 0.22/0.35 % Termbank termtop insertions : 52879
% 0.22/0.35 % Search garbage collected termcells : 13587
% 0.22/0.35
% 0.22/0.35 % -------------------------------------------------
% 0.22/0.35 % User time : 0.048 s
% 0.22/0.35 % System time : 0.012 s
% 0.22/0.35 % Total time : 0.060 s
% 0.22/0.35 % Maximum resident set size: 6816 pages
% 0.22/0.35
% 0.22/0.35 % -------------------------------------------------
% 0.22/0.35 % User time : 0.182 s
% 0.22/0.35 % System time : 0.035 s
% 0.22/0.35 % Total time : 0.217 s
% 0.22/0.35 % Maximum resident set size: 5632 pages
% 0.22/0.35 % E exiting
%------------------------------------------------------------------------------