%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEV236^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:36:20 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 1 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 165 ( 18 ~; 14 |; 10 &; 100 @)
% ( 0 <=>; 22 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 6 ^; 30 !; 7 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
cS: a > $o ).
thf(decl_24,type,
cK: ( a > $o ) > a > $o ).
thf(decl_25,type,
esk1_2: ( a > $o ) > ( a > $o ) > a ).
thf(decl_26,type,
esk2_0: a ).
thf(decl_27,type,
esk1_0: a ).
thf(decl_28,type,
esk3_1: ( a > $o ) > a ).
thf(decl_29,type,
epred2_0: a > $o ).
thf(cTHM91_pme,conjecture,
( ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) )
=> ! [X3: a] :
( ( cK @ cS @ X3 )
=> ( cK
@ ^ [X4: a] :
? [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
=> ( cS @ X6 ) )
& ( X5 @ X4 ) )
@ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.T03tc3h339/E---3.1_1425354.p',cTHM91_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) )
=> ! [X3: a] :
( ( cK @ cS @ X3 )
=> ( cK
@ ^ [X4: a] :
? [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
=> ( cS @ X6 ) )
& ( X5 @ X4 ) )
@ X3 ) ) ),
inference(assume_negation,[status(cth)],[cTHM91_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ! [X1: a > $o,X2: a > $o] :
( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
=> ! [X3: a] :
( ( cK @ X1 @ X3 )
=> ( cK @ X2 @ X3 ) ) )
=> ! [X3: a] :
( ( cK @ cS @ X3 )
=> ( cK
@ ^ [Z0: a] :
? [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
=> ( cS @ X6 ) )
& ( X5 @ Z0 ) )
@ X3 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X12: a > $o,X13: a > $o,X15: a] :
( ( ( X12 @ ( esk1_2 @ X12 @ X13 ) )
| ~ ( cK @ X12 @ X15 )
| ( cK @ X13 @ X15 ) )
& ( ~ ( X13 @ ( esk1_2 @ X12 @ X13 ) )
| ~ ( cK @ X12 @ X15 )
| ( cK @ X13 @ X15 ) )
& ( cK @ cS @ esk2_0 )
& ~ ( cK
@ ^ [Z0: a] :
? [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
=> ( cS @ X6 ) )
& ( X5 @ Z0 ) )
@ esk2_0 ) ),
inference(distribute,[status(thm)],[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_2])])])])])]) ).
thf(c_0_4,negated_conjecture,
~ ( cK
@ ^ [Z0: a] :
? [X87: a > $o] :
( ! [X88: a] :
( ( X87 @ X88 )
=> ( cS @ X88 ) )
& ( X87 @ Z0 ) )
@ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
cK @ cS @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
( ( ^ [Z0: a] :
? [X89: a > $o] :
( ! [X90: a] :
( ( X89 @ X90 )
=> ( cS @ X90 ) )
& ( X89 @ Z0 ) ) )
!= cS ),
inference(ext_sup,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_7,plain,
( ? [X91: a > $o] :
( ! [X92: a] :
( ( X91 @ X92 )
=> ( cS @ X92 ) )
& ( X91 @ esk1_0 ) )
<~> ( cS @ esk1_0 ) ),
inference(neg_ext,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X1: a > $o] :
( ~ ( cS @ ( esk3_1 @ X1 ) )
| ~ ( cS @ esk1_0 )
| ~ ( X1 @ esk1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_9,plain,
( ( cS @ esk1_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: a > $o] :
( ( X1 @ ( esk3_1 @ X1 ) )
| ~ ( cS @ esk1_0 )
| ~ ( X1 @ esk1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
( ( epred2_0 @ esk1_0 )
| ~ ( cS @ ( esk3_1 @ cS ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
thf(c_0_12,plain,
! [X3: a] :
( ( cS @ esk1_0 )
| ( cS @ X3 )
| ~ ( epred2_0 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_7]) ).
thf(c_0_13,plain,
epred2_0 @ esk1_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_9]),c_0_11]) ).
thf(c_0_14,plain,
cS @ esk1_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_15,plain,
! [X1: a > $o] :
( ( X1 @ ( esk3_1 @ X1 ) )
| ~ ( X1 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_14])]) ).
thf(c_0_16,plain,
! [X1: a > $o] :
( ~ ( cS @ ( esk3_1 @ X1 ) )
| ~ ( X1 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_14])]) ).
thf(c_0_17,plain,
cS @ ( esk3_1 @ cS ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
thf(c_0_18,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV236^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n004.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 15:24:22 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 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.T03tc3h339/E---3.1_1425354.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.10/0.24 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting post_as_ho12 with 300s (1) cores
% 0.10/0.24 % Starting new_bool_9 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho4 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho2 with 300s (1) cores
% 0.10/0.24 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.10/0.24 % Starting full_lambda_10 with 300s (1) cores
% 0.10/0.24 % Starting new_ho_8 with 300s (1) cores
% 0.10/0.24 % post_as_ho4 with pid 1425370 completed with status 0
% 0.10/0.24 % Result found by post_as_ho4
% 0.10/0.24 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.10/0.24 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting post_as_ho12 with 300s (1) cores
% 0.10/0.24 % Starting new_bool_9 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho4 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HGUNF-FFSF22-DSSFFMBN
% 0.10/0.24 % partial match(1): HGUNF-FFSF22-SSSFFMBN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 1425375 completed with status 10
% 0.10/0.24 % Starting post_as_ho4 with 31s (1) cores
% 0.10/0.24 % post_as_ho4 with pid 1425381 completed with status 0
% 0.10/0.24 % Result found by post_as_ho4
% 0.10/0.24 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.10/0.24 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting post_as_ho12 with 300s (1) cores
% 0.10/0.24 % Starting new_bool_9 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho1 with 300s (1) cores
% 0.10/0.24 % Starting post_as_ho4 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.24 % No SInE strategy applied
% 0.10/0.24 % Search class: HGUNF-FFSF22-DSSFFMBN
% 0.10/0.24 % partial match(1): HGUNF-FFSF22-SSSFFMBN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 1425375 completed with status 10
% 0.10/0.24 % Starting post_as_ho4 with 31s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24 % Presaturation interreduction done
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 4
% 0.10/0.24 % Removed by relevancy pruning/SinE : 0
% 0.10/0.24 % Initial clauses : 7
% 0.10/0.24 % Removed in clause preprocessing : 3
% 0.10/0.24 % Initial clauses in saturation : 4
% 0.10/0.24 % Processed clauses : 31
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 31
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 0
% 0.10/0.24 % Backward-rewritten : 9
% 0.10/0.24 % Generated clauses : 53
% 0.10/0.24 % ...of the previous two non-redundant : 43
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 4
% 0.10/0.24 % Paramodulations : 34
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 1
% 0.10/0.24 % Equation resolutions : 5
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 19
% 0.10/0.24 % ...of those cached : 14
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 17
% 0.10/0.24 % Positive orientable unit clauses : 6
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 5
% 0.10/0.24 % Non-unit-clauses : 6
% 0.10/0.24 % Current number of unprocessed clauses: 13
% 0.10/0.24 % ...number of literals in the above : 28
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 14
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 27
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 21
% 0.10/0.24 % Non-unit clause-clause subsumptions : 4
% 0.10/0.24 % Unit Clause-clause subsumption calls : 14
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 2
% 0.10/0.24 % BW rewrite match successes : 2
% 0.10/0.24 % Condensation attempts : 31
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 2582
% 0.10/0.24 % Search garbage collected termcells : 170
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.004 s
% 0.10/0.24 % System time : 0.002 s
% 0.10/0.24 % Total time : 0.007 s
% 0.10/0.24 % Maximum resident set size: 3632 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.005 s
% 0.10/0.24 % System time : 0.009 s
% 0.10/0.24 % Total time : 0.013 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------