%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM642^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:16:40 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 4 ~; 0 |; 0 &; 48 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
suc: nat > nat ).
thf(decl_26,type,
pl: nat > nat > nat ).
thf(satz4h,conjecture,
( ( suc @ ( pl @ x @ y ) )
= ( pl @ ( suc @ x ) @ y ) ),
file('/export/starexec/sandbox/tmp/tmp.8F6xVu0Zg2/E---3.1_978293.p',satz4h) ).
thf(satz4d,axiom,
! [X1: nat,X2: nat] :
( ( pl @ ( suc @ X1 ) @ X2 )
= ( suc @ ( pl @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.8F6xVu0Zg2/E---3.1_978293.p',satz4d) ).
thf(c_0_2,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(assume_negation,[status(cth)],[satz4h]) ).
thf(c_0_3,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(fof_nnf,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X5: nat,X6: nat] :
( ( pl @ ( suc @ X5 ) @ X6 )
= ( suc @ ( pl @ X5 @ X6 ) ) ),
inference(variable_rename,[status(thm)],[satz4d]) ).
thf(c_0_6,negated_conjecture,
( ( suc @ ( pl @ x @ y ) )
!= ( pl @ ( suc @ x ) @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X1: nat,X2: nat] :
( ( pl @ ( suc @ X1 ) @ X2 )
= ( suc @ ( pl @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM642^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:25:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.8F6xVu0Zg2/E---3.1_978293.p
% 0.07/0.27 % Version: 3.5.1-ho
% 0.07/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.27 % Starting sh4l with 300s (1) cores
% 0.07/0.27 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.07/0.27 % sh4l with pid 978308 completed with status 0
% 0.07/0.27 % Result found by sh4l
% 0.07/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.27 % Starting sh4l with 300s (1) cores
% 0.07/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.27 % No SInE strategy applied
% 0.07/0.27 % Search class: HUUPF-FFSF21-SFFFFFNN
% 0.07/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.27 % SubtermCWHack with pid 978316 completed with status 0
% 0.07/0.27 % Result found by SubtermCWHack
% 0.07/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.07/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.27 % Starting sh4l with 300s (1) cores
% 0.07/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.27 % No SInE strategy applied
% 0.07/0.27 % Search class: HUUPF-FFSF21-SFFFFFNN
% 0.07/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.27 % Preprocessing time : 0.002 s
% 0.07/0.27
% 0.07/0.27 % Proof found!
% 0.07/0.27 % SZS status Theorem
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.27 % Parsed axioms : 7
% 0.07/0.27 % Removed by relevancy pruning/SinE : 0
% 0.07/0.27 % Initial clauses : 7
% 0.07/0.27 % Removed in clause preprocessing : 5
% 0.07/0.27 % Initial clauses in saturation : 2
% 0.07/0.27 % Processed clauses : 2
% 0.07/0.27 % ...of these trivial : 0
% 0.07/0.27 % ...subsumed : 0
% 0.07/0.27 % ...remaining for further processing : 1
% 0.07/0.27 % Other redundant clauses eliminated : 0
% 0.07/0.27 % Clauses deleted for lack of memory : 0
% 0.07/0.27 % Backward-subsumed : 0
% 0.07/0.27 % Backward-rewritten : 0
% 0.07/0.27 % Generated clauses : 0
% 0.07/0.27 % ...of the previous two non-redundant : 0
% 0.07/0.27 % ...aggressively subsumed : 0
% 0.07/0.27 % Contextual simplify-reflections : 0
% 0.07/0.27 % Paramodulations : 0
% 0.07/0.27 % Factorizations : 0
% 0.07/0.27 % NegExts : 0
% 0.07/0.27 % Equation resolutions : 0
% 0.07/0.27 % Disequality decompositions : 0
% 0.07/0.27 % Total rewrite steps : 1
% 0.07/0.27 % ...of those cached : 0
% 0.07/0.27 % Propositional unsat checks : 0
% 0.07/0.27 % Propositional check models : 0
% 0.07/0.27 % Propositional check unsatisfiable : 0
% 0.07/0.27 % Propositional clauses : 0
% 0.07/0.27 % Propositional clauses after purity: 0
% 0.07/0.27 % Propositional unsat core size : 0
% 0.07/0.27 % Propositional preprocessing time : 0.000
% 0.07/0.27 % Propositional encoding time : 0.000
% 0.07/0.27 % Propositional solver time : 0.000
% 0.07/0.27 % Success case prop preproc time : 0.000
% 0.07/0.27 % Success case prop encoding time : 0.000
% 0.07/0.27 % Success case prop solver time : 0.000
% 0.07/0.27 % Current number of processed clauses : 1
% 0.07/0.27 % Positive orientable unit clauses : 1
% 0.07/0.27 % Positive unorientable unit clauses: 0
% 0.07/0.27 % Negative unit clauses : 0
% 0.07/0.27 % Non-unit-clauses : 0
% 0.07/0.27 % Current number of unprocessed clauses: 0
% 0.07/0.27 % ...number of literals in the above : 0
% 0.07/0.27 % Current number of archived formulas : 0
% 0.07/0.27 % Current number of archived clauses : 0
% 0.07/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.27 % Non-unit clause-clause subsumptions : 0
% 0.07/0.27 % Unit Clause-clause subsumption calls : 0
% 0.07/0.27 % Rewrite failures with RHS unbound : 0
% 0.07/0.27 % BW rewrite match attempts : 0
% 0.07/0.27 % BW rewrite match successes : 0
% 0.07/0.27 % Condensation attempts : 0
% 0.07/0.27 % Condensation successes : 0
% 0.07/0.27 % Termbank termtop insertions : 184
% 0.07/0.27 % Search garbage collected termcells : 9
% 0.07/0.27
% 0.07/0.27 % -------------------------------------------------
% 0.07/0.27 % User time : 0.003 s
% 0.07/0.27 % System time : 0.003 s
% 0.07/0.27 % Total time : 0.006 s
% 0.07/0.27 % Maximum resident set size: 3628 pages
% 0.07/0.27
% 0.07/0.27 % -------------------------------------------------
% 0.07/0.27 % User time : 0.005 s
% 0.07/0.27 % System time : 0.007 s
% 0.07/0.27 % Total time : 0.012 s
% 0.07/0.27 % Maximum resident set size: 4608 pages
% 0.07/0.27 % E exiting
%------------------------------------------------------------------------------