%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEV179^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:36:14 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 80 ( 15 ~; 3 |; 9 &; 53 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 24 ( 9 ^; 6 !; 9 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(decl_24,type,
esk1_0: ( $i > $o ) > $i ).
thf(decl_25,type,
epred1_0: $i > $o ).
thf(cTHM144C_pme,conjecture,
! [X1: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X1 @ ( X1 @ ( cD_FOR_X5309 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.W8ZE2exolH/E---3.1_3290605.p',cTHM144C_pme) ).
thf(cD_FOR_X5309_def,axiom,
( cD_FOR_X5309
= ( ^ [X1: ( $i > $o ) > $i,X2: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( X1 @ X3 ) )
& ( X2
= ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.W8ZE2exolH/E---3.1_3290605.p',cD_FOR_X5309_def) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i] : ( cD_FOR_X5309 @ X1 @ ( X1 @ ( cD_FOR_X5309 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM144C_pme]) ).
thf(c_0_3,plain,
( cD_FOR_X5309
= ( ^ [Z0: ( $i > $o ) > $i,Z1: $i] :
? [X3: $i > $o] :
( ~ ( X3 @ ( Z0 @ X3 ) )
& ( Z1
= ( Z0 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cD_FOR_X5309_def]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: ( $i > $o ) > $i] :
? [X6: $i > $o] :
( ~ ( X6 @ ( X1 @ X6 ) )
& ( ( X1
@ ^ [Z0: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X1 @ X5 ) )
& ( Z0
= ( X1 @ X5 ) ) ) )
= ( X1 @ X6 ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X8: $i > $o] :
( ( X8 @ ( esk1_0 @ X8 ) )
| ( ( esk1_0
@ ^ [Z0: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( esk1_0 @ X5 ) )
& ( Z0
= ( esk1_0 @ X5 ) ) ) )
!= ( esk1_0 @ X8 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ ( esk1_0 @ X3 ) )
| ( ( esk1_0
@ ^ [Z0: $i] :
? [X12: $i > $o] :
( ~ ( X12 @ ( esk1_0 @ X12 ) )
& ( Z0
= ( esk1_0 @ X12 ) ) ) )
!= ( esk1_0 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
? [X13: $i > $o] :
( ~ ( X13 @ ( esk1_0 @ X13 ) )
& ( ( esk1_0
@ ^ [Z0: $i] :
? [X14: $i > $o] :
( ~ ( X14 @ ( esk1_0 @ X14 ) )
& ( Z0
= ( esk1_0 @ X14 ) ) ) )
= ( esk1_0 @ X13 ) ) ),
inference(er,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
( ( esk1_0
@ ^ [Z0: $i] :
? [X15: $i > $o] :
( ~ ( X15 @ ( esk1_0 @ X15 ) )
& ( Z0
= ( esk1_0 @ X15 ) ) ) )
= ( esk1_0 @ epred1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
~ ( epred1_0 @ ( esk1_0 @ epred1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ ( esk1_0 @ X3 ) )
| ( ( esk1_0 @ epred1_0 )
!= ( esk1_0 @ X3 ) ) ),
inference(rw,[status(thm)],[c_0_6,c_0_8]) ).
thf(c_0_11,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_9,c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV179^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:19:39 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.W8ZE2exolH/E---3.1_3290605.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.25 % Starting sh5l with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_6 with 300s (1) cores
% 0.09/0.25 % full_lambda_6 with pid 3290621 completed with status 0
% 0.09/0.25 % Result found by full_lambda_6
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.25 % Starting sh5l with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_6 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.09/0.25 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.09/0.25 % Search class: HHUSF-FFSF00-DHHFMMBN
% 0.09/0.25 % partial match(4): HGUNF-FFSF00-SHHFFMBN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 3290622 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNHHN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ehoh_best_nonlift_nonlambdatoforall with 1500s (5) cores
% 0.09/0.25 % Starting sh5l with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_10 with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_6 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.09/0.25 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.09/0.25 % Search class: HHUSF-FFSF00-DHHFMMBN
% 0.09/0.25 % partial match(4): HGUNF-FFSF00-SHHFFMBN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 3
% 0.09/0.25 % Removed by relevancy pruning/SinE : 1
% 0.09/0.25 % Initial clauses : 1
% 0.09/0.25 % Removed in clause preprocessing : 0
% 0.09/0.25 % Initial clauses in saturation : 1
% 0.09/0.25 % Processed clauses : 5
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 5
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 1
% 0.09/0.25 % Generated clauses : 5
% 0.09/0.25 % ...of the previous two non-redundant : 4
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 2
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 1
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 1
% 0.09/0.25 % ...of those cached : 0
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 3
% 0.09/0.25 % Positive orientable unit clauses : 1
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 1
% 0.09/0.25 % Current number of unprocessed clauses: 0
% 0.09/0.25 % ...number of literals in the above : 0
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 2
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 1
% 0.09/0.25 % BW rewrite match successes : 1
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 907
% 0.09/0.25 % Search garbage collected termcells : 77
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.002 s
% 0.09/0.25 % System time : 0.003 s
% 0.09/0.25 % Total time : 0.004 s
% 0.09/0.25 % Maximum resident set size: 3632 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.004 s
% 0.09/0.25 % System time : 0.007 s
% 0.09/0.25 % Total time : 0.011 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------