%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV272^5 : 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 : n004.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 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 17 equ; 0 cnn)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 142 ( 20 ~; 0 |; 26 &; 76 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 72 ( 36 ^; 20 !; 16 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cSUCC: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).
thf(decl_24,type,
cZERO: ( $i > $o ) > $o ).
thf(cX6007A_pme,conjecture,
( ( ^ [X5: ( $i > $o ) > $o] :
! [X6: ( ( $i > $o ) > $o ) > $o] :
( ( ( X6 @ cZERO )
& ! [X7: ( $i > $o ) > $o] :
( ( X6 @ X7 )
=> ( X6 @ ( cSUCC @ X7 ) ) ) )
=> ( X6 @ X5 ) ) )
= ( ^ [X8: ( $i > $o ) > $o] :
! [X9: ( ( $i > $o ) > $o ) > $o] :
( ( ( X9 @ cZERO )
& ! [X7: ( $i > $o ) > $o] :
( ( X9 @ X7 )
=> ( X9 @ ( cSUCC @ X7 ) ) ) )
=> ( X9 @ X8 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sJ5ljEhRR/E---3.1_1431113.p',cX6007A_pme) ).
thf(cZERO_def,axiom,
( cZERO
= ( ^ [X2: $i > $o] :
~ ? [X3: $i] : ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sJ5ljEhRR/E---3.1_1431113.p',cZERO_def) ).
thf(cSUCC_def,axiom,
( cSUCC
= ( ^ [X1: ( $i > $o ) > $o,X2: $i > $o] :
? [X3: $i] :
( ( X2 @ X3 )
& ( X1
@ ^ [X4: $i] :
( ( X4 != X3 )
& ( X2 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2sJ5ljEhRR/E---3.1_1431113.p',cSUCC_def) ).
thf(c_0_3,negated_conjecture,
( ( ^ [X5: ( $i > $o ) > $o] :
! [X6: ( ( $i > $o ) > $o ) > $o] :
( ( ( X6 @ cZERO )
& ! [X7: ( $i > $o ) > $o] :
( ( X6 @ X7 )
=> ( X6 @ ( cSUCC @ X7 ) ) ) )
=> ( X6 @ X5 ) ) )
!= ( ^ [X8: ( $i > $o ) > $o] :
! [X9: ( ( $i > $o ) > $o ) > $o] :
( ( ( X9 @ cZERO )
& ! [X7: ( $i > $o ) > $o] :
( ( X9 @ X7 )
=> ( X9 @ ( cSUCC @ X7 ) ) ) )
=> ( X9 @ X8 ) ) ) ),
inference(assume_negation,[status(cth)],[cX6007A_pme]) ).
thf(c_0_4,plain,
( cZERO
= ( ^ [Z0: $i > $o] :
~ ? [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[cZERO_def]) ).
thf(c_0_5,plain,
( cSUCC
= ( ^ [Z0: ( $i > $o ) > $o,Z1: $i > $o] :
? [X3: $i] :
( ( Z1 @ X3 )
& ( Z0
@ ^ [Z2: $i] :
( ( Z2 != X3 )
& ( Z1 @ Z2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cSUCC_def]) ).
thf(c_0_6,negated_conjecture,
( ( ^ [Z0: ( $i > $o ) > $o] :
! [X6: ( ( $i > $o ) > $o ) > $o] :
( ( ( X6
@ ^ [Z1: $i > $o] :
~ ? [X10: $i] : ( Z1 @ X10 ) )
& ! [X7: ( $i > $o ) > $o] :
( ( X6 @ X7 )
=> ( X6
@ ^ [Z1: $i > $o] :
? [X11: $i] :
( ( Z1 @ X11 )
& ( X7
@ ^ [Z2: $i] :
( ( Z2 != X11 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X6 @ Z0 ) ) )
!= ( ^ [Z0: ( $i > $o ) > $o] :
! [X9: ( ( $i > $o ) > $o ) > $o] :
( ( ( X9
@ ^ [Z1: $i > $o] :
~ ? [X12: $i] : ( Z1 @ X12 ) )
& ! [X7: ( $i > $o ) > $o] :
( ( X9 @ X7 )
=> ( X9
@ ^ [Z1: $i > $o] :
? [X13: $i] :
( ( Z1 @ X13 )
& ( X7
@ ^ [Z2: $i] :
( ( Z2 != X13 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X9 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4]),c_0_5])]) ).
thf(c_0_7,negated_conjecture,
( ( ^ [Z0: ( $i > $o ) > $o] :
! [X6: ( ( $i > $o ) > $o ) > $o] :
( ( ( X6
@ ^ [Z1: $i > $o] :
~ ? [X10: $i] : ( Z1 @ X10 ) )
& ! [X7: ( $i > $o ) > $o] :
( ( X6 @ X7 )
=> ( X6
@ ^ [Z1: $i > $o] :
? [X11: $i] :
( ( Z1 @ X11 )
& ( X7
@ ^ [Z2: $i] :
( ( Z2 != X11 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X6 @ Z0 ) ) )
!= ( ^ [Z0: ( $i > $o ) > $o] :
! [X9: ( ( $i > $o ) > $o ) > $o] :
( ( ( X9
@ ^ [Z1: $i > $o] :
~ ? [X12: $i] : ( Z1 @ X12 ) )
& ! [X7: ( $i > $o ) > $o] :
( ( X9 @ X7 )
=> ( X9
@ ^ [Z1: $i > $o] :
? [X13: $i] :
( ( Z1 @ X13 )
& ( X7
@ ^ [Z2: $i] :
( ( Z2 != X13 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X9 @ Z0 ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( ^ [Z0: ( $i > $o ) > $o] :
! [X14: ( ( $i > $o ) > $o ) > $o] :
( ( ( X14
@ ^ [Z1: $i > $o] :
~ ? [X15: $i] : ( Z1 @ X15 ) )
& ! [X16: ( $i > $o ) > $o] :
( ( X14 @ X16 )
=> ( X14
@ ^ [Z1: $i > $o] :
? [X17: $i] :
( ( Z1 @ X17 )
& ( X16
@ ^ [Z2: $i] :
( ( Z2 != X17 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X14 @ Z0 ) ) )
!= ( ^ [Z0: ( $i > $o ) > $o] :
! [X18: ( ( $i > $o ) > $o ) > $o] :
( ( ( X18
@ ^ [Z1: $i > $o] :
~ ? [X19: $i] : ( Z1 @ X19 ) )
& ! [X20: ( $i > $o ) > $o] :
( ( X18 @ X20 )
=> ( X18
@ ^ [Z1: $i > $o] :
? [X21: $i] :
( ( Z1 @ X21 )
& ( X20
@ ^ [Z2: $i] :
( ( Z2 != X21 )
& ( Z1 @ Z2 ) ) ) ) ) ) )
=> ( X18 @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
$false,
inference(cn,[status(thm)],[c_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV272^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n004.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 15:30:54 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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.2sJ5ljEhRR/E---3.1_1431113.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % Starting full_lambda_10 with 300s (1) cores
% 0.09/0.24 % Starting full_lambda_6 with 300s (1) cores
% 0.09/0.24 % sh5l with pid 1431127 completed with status 0
% 0.09/0.24 % Result found by sh5l
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.24 % Search class: HUHPF-FFSF00-SHHFMFNN
% 0.09/0.24 % partial match(1): HUHPF-FFSF00-SHHFFFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 1431130 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.24 % Search class: HUHPF-FFSF00-SHHFMFNN
% 0.09/0.24 % partial match(1): HUHPF-FFSF00-SHHFFFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 5
% 0.09/0.24 % Removed by relevancy pruning/SinE : 2
% 0.09/0.24 % Initial clauses : 1
% 0.09/0.24 % Removed in clause preprocessing : 0
% 0.09/0.24 % Initial clauses in saturation : 1
% 0.09/0.24 % Processed clauses : 1
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 0
% 0.09/0.24 % Other redundant clauses eliminated : 0
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 0
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 0
% 0.09/0.24 % ...of the previous two non-redundant : 0
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 0
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 0
% 0.09/0.24 % Equation resolutions : 0
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 0
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 0
% 0.09/0.24 % Positive orientable unit clauses : 0
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 0
% 0.09/0.24 % Non-unit-clauses : 0
% 0.09/0.24 % Current number of unprocessed clauses: 0
% 0.09/0.24 % ...number of literals in the above : 0
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 0
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 0
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 691
% 0.09/0.24 % Search garbage collected termcells : 134
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.004 s
% 0.09/0.24 % System time : 0.001 s
% 0.09/0.24 % Total time : 0.005 s
% 0.09/0.24 % Maximum resident set size: 3640 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.005 s
% 0.09/0.24 % System time : 0.006 s
% 0.09/0.24 % Total time : 0.011 s
% 0.09/0.24 % Maximum resident set size: 4864 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------