%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP077^1 : 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 : n019.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 0.63s 0.39s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% 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 : 24 ( 4 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 3 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
list_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
multiset_a: $tType ).
thf(decl_36,type,
groups1792256535list_a: list_a > a ).
thf(decl_82,type,
comm_m543484931mset_a: multiset_a > a ).
thf(decl_90,type,
mset_a: list_a > multiset_a ).
thf(decl_159,type,
a3: a ).
thf(decl_162,type,
qs2: list_a ).
thf(decl_163,type,
qs: list_a ).
thf(conj_0,conjecture,
( a3
= ( groups1792256535list_a @ qs2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HsNkLzVQuV/E---3.1_1260089.p',conj_0) ).
thf(fact_24_sum__mset__sum__list,axiom,
! [X48: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ X48 ) )
= ( groups1792256535list_a @ X48 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HsNkLzVQuV/E---3.1_1260089.p',fact_24_sum__mset__sum__list) ).
thf(fact_0__092_060open_062mset_Aqs2_A_061_Amset_Aqs_092_060close_062,axiom,
( ( mset_a @ qs2 )
= ( mset_a @ qs ) ),
file('/export/starexec/sandbox2/tmp/tmp.HsNkLzVQuV/E---3.1_1260089.p',fact_0__092_060open_062mset_Aqs2_A_061_Amset_Aqs_092_060close_062) ).
thf(fact_2_a,axiom,
( a3
= ( groups1792256535list_a @ qs ) ),
file('/export/starexec/sandbox2/tmp/tmp.HsNkLzVQuV/E---3.1_1260089.p',fact_2_a) ).
thf(c_0_4,negated_conjecture,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,negated_conjecture,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,plain,
! [X1820: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ X1820 ) )
= ( groups1792256535list_a @ X1820 ) ),
inference(variable_rename,[status(thm)],[fact_24_sum__mset__sum__list]) ).
thf(c_0_7,negated_conjecture,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X1: list_a] :
( ( comm_m543484931mset_a @ ( mset_a @ X1 ) )
= ( groups1792256535list_a @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
( ( mset_a @ qs2 )
= ( mset_a @ qs ) ),
inference(split_conjunct,[status(thm)],[fact_0__092_060open_062mset_Aqs2_A_061_Amset_Aqs_092_060close_062]) ).
thf(c_0_10,plain,
( a3
= ( groups1792256535list_a @ qs ) ),
inference(split_conjunct,[status(thm)],[fact_2_a]) ).
thf(c_0_11,negated_conjecture,
( a3
!= ( groups1792256535list_a @ qs2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]),c_0_10]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP077^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:48:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.27 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.HsNkLzVQuV/E---3.1_1260089.p
% 0.63/0.39 % Version: 3.5.1-ho
% 0.63/0.39 % Preprocessing class: HSLMSMSSSSMNHFA.
% 0.63/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.39 % Starting lpo5_fix with 1500s (5) cores
% 0.63/0.39 % Starting new_bool_3 with 300s (1) cores
% 0.63/0.39 % Starting new_bool_1 with 300s (1) cores
% 0.63/0.39 % Starting new_bool_2 with 300s (1) cores
% 0.63/0.39 % lpo5_fix with pid 1260102 completed with status 0
% 0.63/0.39 % Result found by lpo5_fix
% 0.63/0.39 % Preprocessing class: HSLMSMSSSSMNHFA.
% 0.63/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.39 % Starting lpo5_fix with 1500s (5) cores
% 0.63/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.63/0.39 % No SInE strategy applied
% 0.63/0.39 % Search class: HGHSM-FSLM32-MHFFFSBC
% 0.63/0.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.63/0.39 % Starting SubtermCWHack with 136s (1) cores
% 0.63/0.39 % Starting lpo5_fix with 151s (1) cores
% 0.63/0.39 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.63/0.39 % Starting new_ho_3 with 136s (1) cores
% 0.63/0.39 % Starting sh3 with 136s (1) cores
% 0.63/0.39 % lpo6_lambda_fix with pid 1260111 completed with status 0
% 0.63/0.39 % Result found by lpo6_lambda_fix
% 0.63/0.39 % Preprocessing class: HSLMSMSSSSMNHFA.
% 0.63/0.39 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.63/0.39 % Starting lpo5_fix with 1500s (5) cores
% 0.63/0.39 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.63/0.39 % No SInE strategy applied
% 0.63/0.39 % Search class: HGHSM-FSLM32-MHFFFSBC
% 0.63/0.39 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.63/0.39 % Starting SubtermCWHack with 136s (1) cores
% 0.63/0.39 % Starting lpo5_fix with 151s (1) cores
% 0.63/0.39 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.63/0.39 % Preprocessing time : 0.011 s
% 0.63/0.39
% 0.63/0.39 % Proof found!
% 0.63/0.39 % SZS status Theorem
% 0.63/0.39 % SZS output start CNFRefutation
% See solution above
% 0.63/0.39 % Parsed axioms : 540
% 0.63/0.39 % Removed by relevancy pruning/SinE : 0
% 0.63/0.39 % Initial clauses : 1065
% 0.63/0.39 % Removed in clause preprocessing : 235
% 0.63/0.39 % Initial clauses in saturation : 830
% 0.63/0.39 % Processed clauses : 58
% 0.63/0.39 % ...of these trivial : 1
% 0.63/0.39 % ...subsumed : 4
% 0.63/0.39 % ...remaining for further processing : 53
% 0.63/0.39 % Other redundant clauses eliminated : 16
% 0.63/0.39 % Clauses deleted for lack of memory : 0
% 0.63/0.39 % Backward-subsumed : 0
% 0.63/0.39 % Backward-rewritten : 1
% 0.63/0.39 % Generated clauses : 23
% 0.63/0.39 % ...of the previous two non-redundant : 16
% 0.63/0.39 % ...aggressively subsumed : 0
% 0.63/0.39 % Contextual simplify-reflections : 0
% 0.63/0.39 % Paramodulations : 5
% 0.63/0.39 % Factorizations : 0
% 0.63/0.39 % NegExts : 0
% 0.63/0.39 % Equation resolutions : 18
% 0.63/0.39 % Disequality decompositions : 0
% 0.63/0.39 % Total rewrite steps : 9
% 0.63/0.39 % ...of those cached : 1
% 0.63/0.39 % Propositional unsat checks : 0
% 0.63/0.39 % Propositional check models : 0
% 0.63/0.39 % Propositional check unsatisfiable : 0
% 0.63/0.39 % Propositional clauses : 0
% 0.63/0.39 % Propositional clauses after purity: 0
% 0.63/0.39 % Propositional unsat core size : 0
% 0.63/0.39 % Propositional preprocessing time : 0.000
% 0.63/0.39 % Propositional encoding time : 0.000
% 0.63/0.39 % Propositional solver time : 0.000
% 0.63/0.39 % Success case prop preproc time : 0.000
% 0.63/0.39 % Success case prop encoding time : 0.000
% 0.63/0.39 % Success case prop solver time : 0.000
% 0.63/0.39 % Current number of processed clauses : 38
% 0.63/0.39 % Positive orientable unit clauses : 33
% 0.63/0.39 % Positive unorientable unit clauses: 0
% 0.63/0.39 % Negative unit clauses : 2
% 0.63/0.39 % Non-unit-clauses : 3
% 0.63/0.39 % Current number of unprocessed clauses: 787
% 0.63/0.39 % ...number of literals in the above : 2997
% 0.63/0.39 % Current number of archived formulas : 0
% 0.63/0.39 % Current number of archived clauses : 1
% 0.63/0.39 % Clause-clause subsumption calls (NU) : 9
% 0.63/0.39 % Rec. Clause-clause subsumption calls : 9
% 0.63/0.39 % Non-unit clause-clause subsumptions : 3
% 0.63/0.39 % Unit Clause-clause subsumption calls : 8
% 0.63/0.39 % Rewrite failures with RHS unbound : 0
% 0.63/0.39 % BW rewrite match attempts : 2
% 0.63/0.39 % BW rewrite match successes : 1
% 0.63/0.39 % Condensation attempts : 58
% 0.63/0.39 % Condensation successes : 0
% 0.63/0.39 % Termbank termtop insertions : 78851
% 0.63/0.39 % Search garbage collected termcells : 19238
% 0.63/0.39
% 0.63/0.39 % -------------------------------------------------
% 0.63/0.39 % User time : 0.066 s
% 0.63/0.39 % System time : 0.014 s
% 0.63/0.39 % Total time : 0.080 s
% 0.63/0.39 % Maximum resident set size: 8424 pages
% 0.63/0.39
% 0.63/0.39 % -------------------------------------------------
% 0.63/0.39 % User time : 0.114 s
% 0.63/0.39 % System time : 0.040 s
% 0.63/0.39 % Total time : 0.154 s
% 0.63/0.39 % Maximum resident set size: 5888 pages
% 0.63/0.39 % E exiting
%------------------------------------------------------------------------------