%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG254^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 07:44:45 AM UTC 2026
% Result : Theorem 0.25s 0.32s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 31 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 155 ( 8 ~; 4 |; 9 &; 120 @)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
subst: $tType ).
thf(decl_27,type,
id: subst ).
thf(decl_30,type,
comp: subst > subst > subst ).
thf(decl_84,type,
axassoc: $o ).
thf(decl_97,type,
axidr: $o ).
thf(decl_112,type,
axidl: $o ).
thf(decl_116,type,
substmonoid_lthm: $o ).
thf(decl_121,type,
substmonoid: $o ).
thf(decl_145,type,
esk1_0: subst ).
thf(decl_146,type,
esk2_0: subst ).
thf(decl_147,type,
esk3_0: subst ).
thf(decl_148,type,
esk4_0: subst ).
thf(decl_149,type,
esk5_0: subst ).
thf(thm,conjecture,
substmonoid_lthm,
file('/export/starexec/sandbox2/tmp/tmp.yKrdfs5Jl1/E---3.1_3182570.p',thm) ).
thf(substmonoid_lthm,axiom,
( substmonoid_lthm
<=> ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yKrdfs5Jl1/E---3.1_3182570.p',substmonoid_lthm) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.yKrdfs5Jl1/E---3.1_3182570.p',axidl) ).
thf(axassoc,axiom,
( axassoc
<=> ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yKrdfs5Jl1/E---3.1_3182570.p',axassoc) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.yKrdfs5Jl1/E---3.1_3182570.p',axidr) ).
thf(substmonoid,axiom,
( substmonoid
<=> ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) )
& ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yKrdfs5Jl1/E---3.1_3182570.p',substmonoid) ).
thf(c_0_6,negated_conjecture,
~ substmonoid_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,axiom,
( substmonoid_lthm
= ( ! [X38: subst] :
( ( comp @ id @ X38 )
= X38 )
=> ( ! [X39: subst,X40: subst,X41: subst] :
( ( comp @ ( comp @ X39 @ X40 ) @ X41 )
= ( comp @ X39 @ ( comp @ X40 @ X41 ) ) )
=> ( ! [X42: subst] :
( ( comp @ X42 @ id )
= X42 )
=> ( ! [X43: subst,X44: subst,X45: subst] :
( ( comp @ ( comp @ X43 @ X44 ) @ X45 )
= ( comp @ X43 @ ( comp @ X44 @ X45 ) ) )
& ! [X46: subst] :
( ( comp @ id @ X46 )
= X46 )
& ! [X47: subst] :
( ( comp @ X47 @ id )
= X47 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[substmonoid_lthm,axidl]),axassoc]),axidr]),substmonoid]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X48: subst] :
( ( comp @ id @ X48 )
= X48 )
=> ( ! [X49: subst,X50: subst,X51: subst] :
( ( comp @ ( comp @ X49 @ X50 ) @ X51 )
= ( comp @ X49 @ ( comp @ X50 @ X51 ) ) )
=> ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
=> ( ! [X53: subst,X54: subst,X55: subst] :
( ( comp @ ( comp @ X53 @ X54 ) @ X55 )
= ( comp @ X53 @ ( comp @ X54 @ X55 ) ) )
& ! [X56: subst] :
( ( comp @ id @ X56 )
= X56 )
& ! [X57: subst] :
( ( comp @ X57 @ id )
= X57 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X58: subst,X59: subst,X60: subst,X61: subst,X62: subst] :
( ( ( comp @ id @ X58 )
= X58 )
& ( ( comp @ ( comp @ X59 @ X60 ) @ X61 )
= ( comp @ X59 @ ( comp @ X60 @ X61 ) ) )
& ( ( comp @ X62 @ id )
= X62 )
& ( ( ( comp @ ( comp @ esk1_0 @ esk2_0 ) @ esk3_0 )
!= ( comp @ esk1_0 @ ( comp @ esk2_0 @ esk3_0 ) ) )
| ( ( comp @ id @ esk4_0 )
!= esk4_0 )
| ( ( comp @ esk5_0 @ id )
!= esk5_0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
thf(c_0_10,negated_conjecture,
( ( ( comp @ ( comp @ esk1_0 @ esk2_0 ) @ esk3_0 )
!= ( comp @ esk1_0 @ ( comp @ esk2_0 @ esk3_0 ) ) )
| ( ( comp @ id @ esk4_0 )
!= esk4_0 )
| ( ( comp @ esk5_0 @ id )
!= esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) ),
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
% 0.00/0.03 % Problem : ALG254^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 % Computer : n010.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Sep 29 17:34:18 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.27 Running higher-order theorem proving
% 0.25/0.29 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.yKrdfs5Jl1/E---3.1_3182570.p
% 0.25/0.32 % Version: 3.5.1-ho
% 0.25/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.25/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.32 % Starting post_as_ho10 with 300s (1) cores
% 0.25/0.32 % post_as_ho5 with pid 3182592 completed with status 0
% 0.25/0.32 % Result found by post_as_ho5
% 0.25/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.25/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.25/0.32 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.25/0.32 % Search class: HUHPS-FFSF22-SHFMMFNN
% 0.25/0.32 % partial match(3): HHUPS-FFSF32-SHFMMFNN
% 0.25/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.32 % SubtermCWHack with pid 3182594 completed with status 0
% 0.25/0.32 % Result found by SubtermCWHack
% 0.25/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.25/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.25/0.32 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.25/0.32 % Search class: HUHPS-FFSF22-SHFMMFNN
% 0.25/0.32 % partial match(3): HHUPS-FFSF32-SHFMMFNN
% 0.25/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.32 % Preprocessing time : 0.003 s
% 0.25/0.32
% 0.25/0.32 % Proof found!
% 0.25/0.32 % SZS status Theorem
% 0.25/0.32 % SZS output start CNFRefutation
% See solution above
% 0.25/0.32 % Parsed axioms : 238
% 0.25/0.32 % Removed by relevancy pruning/SinE : 232
% 0.25/0.32 % Initial clauses : 4
% 0.25/0.32 % Removed in clause preprocessing : 0
% 0.25/0.32 % Initial clauses in saturation : 4
% 0.25/0.32 % Processed clauses : 4
% 0.25/0.32 % ...of these trivial : 0
% 0.25/0.32 % ...subsumed : 0
% 0.25/0.32 % ...remaining for further processing : 3
% 0.25/0.32 % Other redundant clauses eliminated : 0
% 0.25/0.32 % Clauses deleted for lack of memory : 0
% 0.25/0.32 % Backward-subsumed : 0
% 0.25/0.32 % Backward-rewritten : 0
% 0.25/0.32 % Generated clauses : 4
% 0.25/0.32 % ...of the previous two non-redundant : 0
% 0.25/0.32 % ...aggressively subsumed : 0
% 0.25/0.32 % Contextual simplify-reflections : 0
% 0.25/0.32 % Paramodulations : 4
% 0.25/0.32 % Factorizations : 0
% 0.25/0.32 % NegExts : 0
% 0.25/0.32 % Equation resolutions : 0
% 0.25/0.32 % Disequality decompositions : 0
% 0.25/0.32 % Total rewrite steps : 9
% 0.25/0.32 % ...of those cached : 0
% 0.25/0.32 % Propositional unsat checks : 0
% 0.25/0.32 % Propositional check models : 0
% 0.25/0.32 % Propositional check unsatisfiable : 0
% 0.25/0.32 % Propositional clauses : 0
% 0.25/0.32 % Propositional clauses after purity: 0
% 0.25/0.32 % Propositional unsat core size : 0
% 0.25/0.32 % Propositional preprocessing time : 0.000
% 0.25/0.32 % Propositional encoding time : 0.000
% 0.25/0.32 % Propositional solver time : 0.000
% 0.25/0.32 % Success case prop preproc time : 0.000
% 0.25/0.32 % Success case prop encoding time : 0.000
% 0.25/0.32 % Success case prop solver time : 0.000
% 0.25/0.32 % Current number of processed clauses : 3
% 0.25/0.32 % Positive orientable unit clauses : 3
% 0.25/0.32 % Positive unorientable unit clauses: 0
% 0.25/0.32 % Negative unit clauses : 0
% 0.25/0.32 % Non-unit-clauses : 0
% 0.25/0.32 % Current number of unprocessed clauses: 0
% 0.25/0.32 % ...number of literals in the above : 0
% 0.25/0.32 % Current number of archived formulas : 0
% 0.25/0.32 % Current number of archived clauses : 0
% 0.25/0.32 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.32 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.32 % Non-unit clause-clause subsumptions : 0
% 0.25/0.32 % Unit Clause-clause subsumption calls : 0
% 0.25/0.32 % Rewrite failures with RHS unbound : 0
% 0.25/0.32 % BW rewrite match attempts : 0
% 0.25/0.32 % BW rewrite match successes : 0
% 0.25/0.32 % Condensation attempts : 0
% 0.25/0.32 % Condensation successes : 0
% 0.25/0.32 % Termbank termtop insertions : 5289
% 0.25/0.32 % Search garbage collected termcells : 1963
% 0.25/0.32
% 0.25/0.32 % -------------------------------------------------
% 0.25/0.32 % User time : 0.007 s
% 0.25/0.32 % System time : 0.004 s
% 0.25/0.32 % Total time : 0.011 s
% 0.25/0.32 % Maximum resident set size: 4492 pages
% 0.25/0.32
% 0.25/0.32 % -------------------------------------------------
% 0.25/0.32 % User time : 0.013 s
% 0.25/0.32 % System time : 0.006 s
% 0.25/0.32 % Total time : 0.019 s
% 0.25/0.32 % Maximum resident set size: 4864 pages
% 0.25/0.32 % E exiting
%------------------------------------------------------------------------------