%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV282^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:35:19 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 13 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 21 ~; 1 |; 18 &; 53 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 52 ( 27 ^; 9 !; 16 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cNAT: ( ( $i > $o ) > $o ) > $o ).
thf(decl_24,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
cZERO: ( $i > $o ) > $o ).
thf(decl_26,type,
epred1_0: ( ( $i > $o ) > $o ) > $o ).
thf(cNAT_def,axiom,
( cNAT
= ( ^ [X3: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5 @ cZERO )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5 @ ( cSUCC @ X6 ) ) ) )
=> ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qe0i9Q9sjO/E---3.1_463252.p',cNAT_def) ).
thf(cSUCC_def,axiom,
( cSUCC
= ( ^ [X3: ( $i > $o ) > $o,X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ( X3
@ ^ [X4: $i] :
( ( X4 != X2 )
& ( X1 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qe0i9Q9sjO/E---3.1_463252.p',cSUCC_def) ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X1: $i > $o] :
~ ? [X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Qe0i9Q9sjO/E---3.1_463252.p',cZERO_def) ).
thf(cTTTP6100,conjecture,
cNAT @ cZERO,
file('/export/starexec/sandbox/tmp/tmp.Qe0i9Q9sjO/E---3.1_463252.p',cTTTP6100) ).
thf(c_0_4,plain,
( cNAT
= ( ^ [Z0: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5
@ ^ [Z1: $i > $o] :
~ ? [X7: $i] : ( Z1 @ X7 ) )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5
@ ^ [Z1: $i > $o] :
? [X8: $i] :
( ( Z1 @ X8 )
& ( X6
@ ^ [Z2: $i] :
( ( Z2 != X8 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X5 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[cNAT_def]) ).
thf(c_0_5,plain,
( cSUCC
= ( ^ [Z0: ( $i > $o ) > $o,Z1: $i > $o] :
? [X2: $i] :
( ( Z1 @ X2 )
& ( Z0
@ ^ [Z2: $i] :
( ( Z2 != X2 )
& ( Z1 @ Z2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cSUCC_def]) ).
thf(c_0_6,plain,
( cZERO
= ( ^ [Z0: $i > $o] :
~ ? [X2: $i] : ( Z0 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[cZERO_def]) ).
thf(c_0_7,negated_conjecture,
~ ( cNAT @ cZERO ),
inference(assume_negation,[status(cth)],[cTTTP6100]) ).
thf(c_0_8,plain,
( cNAT
= ( ^ [Z0: ( $i > $o ) > $o] :
! [X5: ( ( $i > $o ) > $o ) > $o] :
( ( ( X5
@ ^ [Z1: $i > $o] :
~ ? [X7: $i] : ( Z1 @ X7 ) )
& ! [X6: ( $i > $o ) > $o] :
( ( X5 @ X6 )
=> ( X5
@ ^ [Z1: $i > $o] :
? [X8: $i] :
( ( Z1 @ X8 )
& ( X6
@ ^ [Z2: $i] :
( ( Z2 != X8 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X5 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ! [X10: ( ( $i > $o ) > $o ) > $o] :
( ( ( X10
@ ^ [Z0: $i > $o] :
~ ? [X11: $i] : ( Z0 @ X11 ) )
& ! [X12: ( $i > $o ) > $o] :
( ( X10 @ X12 )
=> ( X10
@ ^ [Z0: $i > $o] :
? [X13: $i] :
( ( Z0 @ X13 )
& ( X12
@ ^ [Z1: $i] :
( ( Z1 != X13 )
& ( Z0 @ Z1 ) ) ) ) ) ) )
=> ( X10
@ ^ [Z0: $i > $o] :
~ ? [X9: $i] : ( Z0 @ X9 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X15: ( $i > $o ) > $o] :
( ( epred1_0
@ ^ [Z0: $i > $o] :
~ ? [X11: $i] : ( Z0 @ X11 ) )
& ( ~ ( epred1_0 @ X15 )
| ( epred1_0
@ ^ [Z0: $i > $o] :
? [X13: $i] :
( ( Z0 @ X13 )
& ( X15
@ ^ [Z1: $i] :
( ( Z1 != X13 )
& ( Z0 @ Z1 ) ) ) ) ) )
& ~ ( epred1_0
@ ^ [Z0: $i > $o] :
~ ? [X9: $i] : ( Z0 @ X9 ) ) ),
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_9])])])])]) ).
thf(c_0_11,negated_conjecture,
~ ( epred1_0
@ ^ [Z0: $i > $o] :
~ ? [X16: $i] : ( Z0 @ X16 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( epred1_0
@ ^ [Z0: $i > $o] :
~ ? [X17: $i] : ( Z0 @ X17 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV282^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:26:37 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.Qe0i9Q9sjO/E---3.1_463252.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.08/0.25 % Starting full_lambda_6 with 300s (1) cores
% 0.08/0.25 % full_lambda_10 with pid 463283 completed with status 0
% 0.08/0.25 % Result found by full_lambda_10
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.08/0.25 % Search class: HHUNF-FFSF00-DHHFMFBN
% 0.08/0.25 % partial match(3): HHUNF-FFSF00-SHHSMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 463289 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.08/0.25 % Starting sh5l with 300s (1) cores
% 0.08/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.08/0.25 % Search class: HHUNF-FFSF00-DHHFMFBN
% 0.08/0.25 % partial match(3): HHUNF-FFSF00-SHHSMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 7
% 0.08/0.25 % Removed by relevancy pruning/SinE : 3
% 0.08/0.25 % Initial clauses : 3
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 3
% 0.08/0.25 % Processed clauses : 2
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 1
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 0
% 0.08/0.25 % ...of the previous two non-redundant : 0
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 0
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 1
% 0.08/0.25 % ...of those cached : 0
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 1
% 0.08/0.25 % Positive orientable unit clauses : 1
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 0
% 0.08/0.25 % Non-unit-clauses : 0
% 0.08/0.25 % Current number of unprocessed clauses: 1
% 0.08/0.25 % ...number of literals in the above : 2
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 0
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 535
% 0.08/0.25 % Search garbage collected termcells : 137
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.002 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.004 s
% 0.08/0.25 % Maximum resident set size: 3640 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.003 s
% 0.08/0.25 % System time : 0.007 s
% 0.08/0.25 % Total time : 0.010 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------