%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP078^1 : 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 : n013.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 08:04:17 AM UTC 2026
% Result : Theorem 0.30s 0.39s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 14 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 177 ( 6 ~; 2 |; 0 &; 168 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
set_nat: $tType ).
thf(decl_sort3,type,
a: $tType ).
thf(decl_sort4,type,
list_a: $tType ).
thf(decl_sort5,type,
multiset_nat: $tType ).
thf(decl_sort6,type,
multiset_a: $tType ).
thf(decl_46,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(decl_54,type,
zero_zero_nat: nat ).
thf(decl_70,type,
nth_a: list_a > nat > a ).
thf(decl_73,type,
image_mset_nat_nat: ( nat > nat ) > multiset_nat > multiset_nat ).
thf(decl_74,type,
image_mset_nat_a: ( nat > a ) > multiset_nat > multiset_a ).
thf(decl_78,type,
mset_a: list_a > multiset_a ).
thf(decl_80,type,
mset_set_nat: set_nat > multiset_nat ).
thf(decl_88,type,
size_size_list_a: list_a > nat ).
thf(decl_105,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(decl_109,type,
set_or562006527an_nat: nat > nat > set_nat ).
thf(decl_118,type,
f: nat > nat ).
thf(decl_119,type,
xs: list_a ).
thf(decl_120,type,
ys: list_a ).
thf(conj_0,conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GjteitcV61/E---3.1_2570883.p',conj_0) ).
thf(fact_71_image__mset__mset__set,axiom,
! [X74: nat > nat,X72: set_nat] :
( ( inj_on_nat_nat @ X74 @ X72 )
=> ( ( image_mset_nat_nat @ X74 @ ( mset_set_nat @ X72 ) )
= ( mset_set_nat @ ( image_nat_nat @ X74 @ X72 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GjteitcV61/E---3.1_2570883.p',fact_71_image__mset__mset__set) ).
thf(fact_3__C2_C,axiom,
( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GjteitcV61/E---3.1_2570883.p',fact_3__C2_C) ).
thf(fact_0__C1_C,axiom,
inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ),
file('/export/starexec/sandbox2/tmp/tmp.GjteitcV61/E---3.1_2570883.p',fact_0__C1_C) ).
thf(fact_1_calculation,axiom,
( ( mset_a @ xs )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GjteitcV61/E---3.1_2570883.p',fact_1_calculation) ).
thf(c_0_5,negated_conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_6,plain,
! [X595: nat > nat,X596: set_nat] :
( ~ ( inj_on_nat_nat @ X595 @ X596 )
| ( ( image_mset_nat_nat @ X595 @ ( mset_set_nat @ X596 ) )
= ( mset_set_nat @ ( image_nat_nat @ X595 @ X596 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_71_image__mset__mset__set])])]) ).
thf(c_0_7,negated_conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X13: nat > nat,X72: set_nat] :
( ( ( image_mset_nat_nat @ X13 @ ( mset_set_nat @ X72 ) )
= ( mset_set_nat @ ( image_nat_nat @ X13 @ X72 ) ) )
| ~ ( inj_on_nat_nat @ X13 @ X72 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
( ( image_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) )
= ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ),
inference(split_conjunct,[status(thm)],[fact_3__C2_C]) ).
thf(c_0_10,plain,
inj_on_nat_nat @ f @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ),
inference(split_conjunct,[status(thm)],[fact_0__C1_C]) ).
thf(c_0_11,negated_conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
( ( mset_a @ xs )
= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[fact_1_calculation]) ).
thf(c_0_13,plain,
( ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) )
= ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
thf(c_0_14,negated_conjecture,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( image_mset_nat_nat @ f @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ xs ) ) ) ) )
!= ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
( ( image_mset_nat_a @ ( nth_a @ ys ) @ ( mset_set_nat @ ( set_or562006527an_nat @ zero_zero_nat @ ( size_size_list_a @ ys ) ) ) )
= ( mset_a @ xs ) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13]),c_0_15]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP078^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n013.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:47:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.23/0.32 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.GjteitcV61/E---3.1_2570883.p
% 0.30/0.38 % Version: 3.5.1-ho
% 0.30/0.38 % Preprocessing class: HSLSSMSSSSSNHSA.
% 0.30/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.38 % Starting full_lambda_9 with 1500s (5) cores
% 0.30/0.38 % Starting new_ho_11 with 300s (1) cores
% 0.30/0.38 % Starting sh2l with 300s (1) cores
% 0.30/0.38 % Starting new_bool_6 with 300s (1) cores
% 0.30/0.38 % new_bool_6 with pid 2570899 completed with status 0
% 0.30/0.38 % Result found by new_bool_6
% 0.30/0.38 % Preprocessing class: HSLSSMSSSSSNHSA.
% 0.30/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.38 % Starting full_lambda_9 with 1500s (5) cores
% 0.30/0.38 % Starting new_ho_11 with 300s (1) cores
% 0.30/0.38 % Starting sh2l with 300s (1) cores
% 0.30/0.38 % Starting new_bool_6 with 300s (1) cores
% 0.30/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.30/0.38 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.30/0.38 % Search class: HGHSS-FFMS31-MHSFFSBN
% 0.30/0.38 % partial match(2): HGHSS-FFMS21-MSSFFSBN
% 0.30/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.30/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.30/0.38 % SubtermCWHack with pid 2570900 completed with status 0
% 0.30/0.39 % Result found by SubtermCWHack
% 0.30/0.39 % Preprocessing class: HSLSSMSSSSSNHSA.
% 0.30/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.39 % Starting full_lambda_9 with 1500s (5) cores
% 0.30/0.39 % Starting new_ho_11 with 300s (1) cores
% 0.30/0.39 % Starting sh2l with 300s (1) cores
% 0.30/0.39 % Starting new_bool_6 with 300s (1) cores
% 0.30/0.39 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1.0,,1,20000,1.0))
% 0.30/0.39 % SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 0.30/0.39 % Search class: HGHSS-FFMS31-MHSFFSBN
% 0.30/0.39 % partial match(2): HGHSS-FFMS21-MSSFFSBN
% 0.30/0.39 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.30/0.39 % Starting SubtermCWHack with 28s (1) cores
% 0.30/0.39 % Preprocessing time : 0.003 s
% 0.30/0.39
% 0.30/0.39 % Proof found!
% 0.30/0.39 % SZS status Theorem
% 0.30/0.39 % SZS output start CNFRefutation
% See solution above
% 0.30/0.39 % Parsed axioms : 469
% 0.30/0.39 % Removed by relevancy pruning/SinE : 432
% 0.30/0.39 % Initial clauses : 63
% 0.30/0.39 % Removed in clause preprocessing : 7
% 0.30/0.39 % Initial clauses in saturation : 56
% 0.30/0.39 % Processed clauses : 154
% 0.30/0.39 % ...of these trivial : 1
% 0.30/0.39 % ...subsumed : 66
% 0.30/0.39 % ...remaining for further processing : 86
% 0.30/0.39 % Other redundant clauses eliminated : 14
% 0.30/0.39 % Clauses deleted for lack of memory : 0
% 0.30/0.39 % Backward-subsumed : 3
% 0.30/0.39 % Backward-rewritten : 1
% 0.30/0.39 % Generated clauses : 385
% 0.30/0.39 % ...of the previous two non-redundant : 359
% 0.30/0.39 % ...aggressively subsumed : 0
% 0.30/0.39 % Contextual simplify-reflections : 0
% 0.30/0.39 % Paramodulations : 355
% 0.30/0.39 % Factorizations : 12
% 0.30/0.39 % NegExts : 0
% 0.30/0.39 % Equation resolutions : 18
% 0.30/0.39 % Disequality decompositions : 0
% 0.30/0.39 % Total rewrite steps : 8
% 0.30/0.39 % ...of those cached : 3
% 0.30/0.39 % Propositional unsat checks : 0
% 0.30/0.39 % Propositional check models : 0
% 0.30/0.39 % Propositional check unsatisfiable : 0
% 0.30/0.39 % Propositional clauses : 0
% 0.30/0.39 % Propositional clauses after purity: 0
% 0.30/0.39 % Propositional unsat core size : 0
% 0.30/0.39 % Propositional preprocessing time : 0.000
% 0.30/0.39 % Propositional encoding time : 0.000
% 0.30/0.39 % Propositional solver time : 0.000
% 0.30/0.39 % Success case prop preproc time : 0.000
% 0.30/0.39 % Success case prop encoding time : 0.000
% 0.30/0.39 % Success case prop solver time : 0.000
% 0.30/0.39 % Current number of processed clauses : 74
% 0.30/0.39 % Positive orientable unit clauses : 6
% 0.30/0.39 % Positive unorientable unit clauses: 0
% 0.30/0.39 % Negative unit clauses : 1
% 0.30/0.39 % Non-unit-clauses : 67
% 0.30/0.39 % Current number of unprocessed clauses: 260
% 0.30/0.39 % ...number of literals in the above : 1314
% 0.30/0.39 % Current number of archived formulas : 0
% 0.30/0.39 % Current number of archived clauses : 4
% 0.30/0.39 % Clause-clause subsumption calls (NU) : 962
% 0.30/0.39 % Rec. Clause-clause subsumption calls : 423
% 0.30/0.39 % Non-unit clause-clause subsumptions : 49
% 0.30/0.39 % Unit Clause-clause subsumption calls : 1
% 0.30/0.39 % Rewrite failures with RHS unbound : 0
% 0.30/0.39 % BW rewrite match attempts : 1
% 0.30/0.39 % BW rewrite match successes : 1
% 0.30/0.39 % Condensation attempts : 0
% 0.30/0.39 % Condensation successes : 0
% 0.30/0.39 % Termbank termtop insertions : 16511
% 0.30/0.39 % Search garbage collected termcells : 4053
% 0.30/0.39
% 0.30/0.39 % -------------------------------------------------
% 0.30/0.39 % User time : 0.030 s
% 0.30/0.39 % System time : 0.007 s
% 0.30/0.39 % Total time : 0.037 s
% 0.30/0.39 % Maximum resident set size: 4740 pages
% 0.30/0.39
% 0.30/0.39 % -------------------------------------------------
% 0.30/0.39 % User time : 0.043 s
% 0.30/0.39 % System time : 0.012 s
% 0.30/0.39 % Total time : 0.056 s
% 0.30/0.39 % Maximum resident set size: 5632 pages
% 0.30/0.39 % E exiting
%------------------------------------------------------------------------------