%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:17:11 AM UTC 2026
% Result : Theorem 0.23s 0.35s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 26 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 202 ( 5 ~; 0 |; 13 &; 177 @)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
n: $tType ).
thf(decl_23,type,
c0: n ).
thf(decl_24,type,
cS: n > n ).
thf(decl_25,type,
c_plus: n > n > n ).
thf(decl_26,type,
c_star: n > n > n ).
thf(decl_27,type,
cPA_1: $o ).
thf(decl_28,type,
cPA_2: $o ).
thf(decl_29,type,
cPA_3: $o ).
thf(decl_30,type,
cPA_4: $o ).
thf(cPA_THM1,conjecture,
( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rAehjb3V97/E---3.1_3948980.p',cPA_THM1) ).
thf(cPA_1_def,axiom,
( cPA_1
<=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.rAehjb3V97/E---3.1_3948980.p',cPA_1_def) ).
thf(cPA_2_def,axiom,
( cPA_2
<=> ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rAehjb3V97/E---3.1_3948980.p',cPA_2_def) ).
thf(cPA_3_def,axiom,
( cPA_3
<=> ! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.rAehjb3V97/E---3.1_3948980.p',cPA_3_def) ).
thf(cPA_4_def,axiom,
( cPA_4
<=> ! [X1: n,X2: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rAehjb3V97/E---3.1_3948980.p',cPA_4_def) ).
thf(c_0_5,negated_conjecture,
~ ( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPA_THM1]) ).
thf(c_0_6,negated_conjecture,
~ ( ( ! [X9: n] :
( ( c_plus @ X9 @ c0 )
= X9 )
& ! [X10: n,X11: n] :
( ( c_plus @ X10 @ ( cS @ X11 ) )
= ( cS @ ( c_plus @ X10 @ X11 ) ) )
& ! [X12: n] :
( ( c_star @ X12 @ c0 )
= c0 )
& ! [X13: n,X14: n] :
( ( c_star @ X13 @ ( cS @ X14 ) )
= ( c_plus @ ( c_star @ X13 @ X14 ) @ X13 ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,cPA_1_def]),cPA_2_def]),cPA_3_def]),cPA_4_def]) ).
thf(c_0_7,negated_conjecture,
! [X15: n,X16: n,X17: n,X18: n,X19: n,X20: n] :
( ( ( c_plus @ X15 @ c0 )
= X15 )
& ( ( c_plus @ X16 @ ( cS @ X17 ) )
= ( cS @ ( c_plus @ X16 @ X17 ) ) )
& ( ( c_star @ X18 @ c0 )
= c0 )
& ( ( c_star @ X19 @ ( cS @ X20 ) )
= ( c_plus @ ( c_star @ X19 @ X20 ) @ X19 ) )
& ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X2: n,X1: n] :
( ( c_star @ X1 @ ( cS @ X2 ) )
= ( c_plus @ ( c_star @ X1 @ X2 ) @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: n,X2: n] :
( ( cS @ ( c_plus @ ( c_star @ ( cS @ X1 ) @ X2 ) @ X1 ) )
= ( c_star @ ( cS @ X1 ) @ ( cS @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: n,X2: n] :
( ( cS @ ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ X1 ) ) @ X2 ) @ X1 ) ) )
= ( c_star @ ( cS @ ( cS @ X1 ) ) @ ( cS @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
! [X1: n] :
( ( c_star @ X1 @ c0 )
= c0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_15,negated_conjecture,
! [X1: n] :
( ( cS @ ( cS @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ X1 ) ) )
= ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: n] :
( ( c_star @ X1 @ ( cS @ c0 ) )
= ( c_plus @ c0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
thf(c_0_17,negated_conjecture,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_8]),c_0_8]),c_0_12]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_8]),c_0_8]),c_0_12]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM830^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n009.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 13:04:00 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.31 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.rAehjb3V97/E---3.1_3948980.p
% 0.23/0.35 % Version: 3.5.1-ho
% 0.23/0.35 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.35 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.35 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.35 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.35 % post_as_ho2 with pid 3948996 completed with status 0
% 0.23/0.35 % Result found by post_as_ho2
% 0.23/0.35 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.35 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.35 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.35 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.35 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.35 % No SInE strategy applied
% 0.23/0.35 % Search class: HUUPM-FFSF21-MFFFMFNN
% 0.23/0.35 % partial match(2): FUUPM-FFSF21-MFFFFFNN
% 0.23/0.35 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.35 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.35 % SubtermCWHack with pid 3949002 completed with status 0
% 0.23/0.35 % Result found by SubtermCWHack
% 0.23/0.35 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.23/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.23/0.35 % Starting post_as_ho8 with 300s (1) cores
% 0.23/0.35 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.35 % Starting post_as_ho2 with 300s (1) cores
% 0.23/0.35 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.35 % No SInE strategy applied
% 0.23/0.35 % Search class: HUUPM-FFSF21-MFFFMFNN
% 0.23/0.35 % partial match(2): FUUPM-FFSF21-MFFFFFNN
% 0.23/0.35 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.35 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.35 % Preprocessing time : 0.001 s
% 0.23/0.35
% 0.23/0.35 % Proof found!
% 0.23/0.35 % SZS status Theorem
% 0.23/0.35 % SZS output start CNFRefutation
% See solution above
% 0.23/0.35 % Parsed axioms : 14
% 0.23/0.35 % Removed by relevancy pruning/SinE : 0
% 0.23/0.35 % Initial clauses : 14
% 0.23/0.35 % Removed in clause preprocessing : 9
% 0.23/0.35 % Initial clauses in saturation : 5
% 0.23/0.35 % Processed clauses : 16
% 0.23/0.35 % ...of these trivial : 2
% 0.23/0.35 % ...subsumed : 0
% 0.23/0.35 % ...remaining for further processing : 14
% 0.23/0.35 % Other redundant clauses eliminated : 0
% 0.23/0.35 % Clauses deleted for lack of memory : 0
% 0.23/0.35 % Backward-subsumed : 0
% 0.23/0.35 % Backward-rewritten : 0
% 0.23/0.35 % Generated clauses : 59
% 0.23/0.35 % ...of the previous two non-redundant : 42
% 0.23/0.35 % ...aggressively subsumed : 0
% 0.23/0.35 % Contextual simplify-reflections : 0
% 0.23/0.35 % Paramodulations : 59
% 0.23/0.35 % Factorizations : 0
% 0.23/0.35 % NegExts : 0
% 0.23/0.35 % Equation resolutions : 0
% 0.23/0.35 % Disequality decompositions : 0
% 0.23/0.35 % Total rewrite steps : 82
% 0.23/0.35 % ...of those cached : 38
% 0.23/0.35 % Propositional unsat checks : 0
% 0.23/0.35 % Propositional check models : 0
% 0.23/0.35 % Propositional check unsatisfiable : 0
% 0.23/0.35 % Propositional clauses : 0
% 0.23/0.35 % Propositional clauses after purity: 0
% 0.23/0.35 % Propositional unsat core size : 0
% 0.23/0.35 % Propositional preprocessing time : 0.000
% 0.23/0.35 % Propositional encoding time : 0.000
% 0.23/0.35 % Propositional solver time : 0.000
% 0.23/0.35 % Success case prop preproc time : 0.000
% 0.23/0.35 % Success case prop encoding time : 0.000
% 0.23/0.35 % Success case prop solver time : 0.000
% 0.23/0.35 % Current number of processed clauses : 14
% 0.23/0.35 % Positive orientable unit clauses : 13
% 0.23/0.35 % Positive unorientable unit clauses: 0
% 0.23/0.35 % Negative unit clauses : 1
% 0.23/0.35 % Non-unit-clauses : 0
% 0.23/0.35 % Current number of unprocessed clauses: 24
% 0.23/0.35 % ...number of literals in the above : 24
% 0.23/0.35 % Current number of archived formulas : 0
% 0.23/0.35 % Current number of archived clauses : 0
% 0.23/0.35 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.35 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.35 % Non-unit clause-clause subsumptions : 0
% 0.23/0.35 % Unit Clause-clause subsumption calls : 0
% 0.23/0.35 % Rewrite failures with RHS unbound : 0
% 0.23/0.35 % BW rewrite match attempts : 0
% 0.23/0.35 % BW rewrite match successes : 0
% 0.23/0.35 % Condensation attempts : 0
% 0.23/0.35 % Condensation successes : 0
% 0.23/0.35 % Termbank termtop insertions : 1771
% 0.23/0.35 % Search garbage collected termcells : 116
% 0.23/0.35
% 0.23/0.35 % -------------------------------------------------
% 0.23/0.35 % User time : 0.004 s
% 0.23/0.35 % System time : 0.003 s
% 0.23/0.35 % Total time : 0.007 s
% 0.23/0.35 % Maximum resident set size: 3632 pages
% 0.23/0.35
% 0.23/0.35 % -------------------------------------------------
% 0.23/0.35 % User time : 0.005 s
% 0.23/0.35 % System time : 0.008 s
% 0.23/0.35 % Total time : 0.014 s
% 0.23/0.35 % Maximum resident set size: 4864 pages
% 0.23/0.35 % E exiting
%------------------------------------------------------------------------------