%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO272^5 : 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 : n018.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 08:42:41 AM UTC 2026
% Result : Theorem 244.83s 31.73s
% Output : CNFRefutation 244.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 40 ( 0 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 285 ( 21 ~; 22 |; 17 &; 213 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 41 ( 4 ^; 37 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cHALF: $i > $i > $o ).
thf(decl_24,type,
cDOUBLE: $i > $i > $o ).
thf(decl_25,type,
cS: $i > $i ).
thf(decl_26,type,
c0: $i ).
thf(decl_27,type,
esk1_3: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_28,type,
esk2_3: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_29,type,
epred1_2: $i > $i > $i > $i > $o ).
thf(decl_30,type,
esk3_0: $i ).
thf(decl_31,type,
esk4_0: $i ).
thf(cTHM301A,conjecture,
( ( ! [X1: $i,X2: $i] :
( ( cDOUBLE @ X1 @ X2 )
<=> ! [X3: $i > $i > $o] :
( ( ( X3 @ c0 @ c0 )
& ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ( X3 @ ( cS @ X4 ) @ ( cS @ ( cS @ X5 ) ) ) ) )
=> ( X3 @ X1 @ X2 ) ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ ( cS @ c0 ) @ c0 )
& ! [X4: $i,X5: $i] :
( ( cHALF @ X4 @ X5 )
=> ( cHALF @ ( cS @ ( cS @ X4 ) ) @ ( cS @ X5 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( cDOUBLE @ X1 @ X2 )
=> ( cHALF @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.L2Uz7qzrUE/E---3.1_323010.p',cTHM301A) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i] :
( ( cDOUBLE @ X1 @ X2 )
<=> ! [X3: $i > $i > $o] :
( ( ( X3 @ c0 @ c0 )
& ! [X4: $i,X5: $i] :
( ( X3 @ X4 @ X5 )
=> ( X3 @ ( cS @ X4 ) @ ( cS @ ( cS @ X5 ) ) ) ) )
=> ( X3 @ X1 @ X2 ) ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ ( cS @ c0 ) @ c0 )
& ! [X4: $i,X5: $i] :
( ( cHALF @ X4 @ X5 )
=> ( cHALF @ ( cS @ ( cS @ X4 ) ) @ ( cS @ X5 ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( cDOUBLE @ X1 @ X2 )
=> ( cHALF @ X2 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cTHM301A]) ).
thf(c_0_2,negated_conjecture,
! [X15: $i,X16: $i,X17: $i > $i > $o,X20: $i,X21: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
( ( ( X17 @ ( esk1_3 @ X15 @ X16 @ X17 ) @ ( esk2_3 @ X15 @ X16 @ X17 ) )
| ~ ( X17 @ c0 @ c0 )
| ( X17 @ X15 @ X16 )
| ~ ( cDOUBLE @ X15 @ X16 ) )
& ( ~ ( X17 @ ( cS @ ( esk1_3 @ X15 @ X16 @ X17 ) ) @ ( cS @ ( cS @ ( esk2_3 @ X15 @ X16 @ X17 ) ) ) )
| ~ ( X17 @ c0 @ c0 )
| ( X17 @ X15 @ X16 )
| ~ ( cDOUBLE @ X15 @ X16 ) )
& ( ( epred1_2 @ X20 @ X21 @ c0 @ c0 )
| ( cDOUBLE @ X20 @ X21 ) )
& ( ~ ( epred1_2 @ X20 @ X21 @ X23 @ X24 )
| ( epred1_2 @ X20 @ X21 @ ( cS @ X23 ) @ ( cS @ ( cS @ X24 ) ) )
| ( cDOUBLE @ X20 @ X21 ) )
& ( ~ ( epred1_2 @ X20 @ X21 @ X20 @ X21 )
| ( cDOUBLE @ X20 @ X21 ) )
& ( cHALF @ c0 @ c0 )
& ( cHALF @ ( cS @ c0 ) @ c0 )
& ( ~ ( cHALF @ X25 @ X26 )
| ( cHALF @ ( cS @ ( cS @ X25 ) ) @ ( cS @ X26 ) ) )
& ( cDOUBLE @ esk3_0 @ esk4_0 )
& ~ ( cHALF @ esk4_0 @ esk3_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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $i,X3: $i > $i > $o,X2: $i] :
( ( X3 @ X1 @ X2 )
| ~ ( X3 @ ( cS @ ( esk1_3 @ X1 @ X2 @ X3 ) ) @ ( cS @ ( cS @ ( esk2_3 @ X1 @ X2 @ X3 ) ) ) )
| ~ ( X3 @ c0 @ c0 )
| ~ ( cDOUBLE @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
cDOUBLE @ esk3_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i,X3: $i > $i > $o,X2: $i] :
( ( X3 @ ( esk1_3 @ X1 @ X2 @ X3 ) @ ( esk2_3 @ X1 @ X2 @ X3 ) )
| ( X3 @ X1 @ X2 )
| ~ ( X3 @ c0 @ c0 )
| ~ ( cDOUBLE @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i > $i > $o] :
( ( X3 @ esk3_0 @ esk4_0 )
| ~ ( X3 @ ( cS @ ( esk1_3 @ esk3_0 @ esk4_0 @ X3 ) ) @ ( cS @ ( cS @ ( esk2_3 @ esk3_0 @ esk4_0 @ X3 ) ) ) )
| ~ ( X3 @ c0 @ c0 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cHALF @ ( cS @ ( cS @ X1 ) ) @ ( cS @ X2 ) )
| ~ ( cHALF @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
cHALF @ c0 @ c0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
~ ( cHALF @ esk4_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i > $i > $o] :
( ( X3 @ ( esk1_3 @ esk3_0 @ esk4_0 @ X3 ) @ ( esk2_3 @ esk3_0 @ esk4_0 @ X3 ) )
| ( X3 @ esk3_0 @ esk4_0 )
| ~ ( X3 @ c0 @ c0 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
thf(c_0_11,negated_conjecture,
~ ( cHALF
@ ( esk2_3 @ esk3_0 @ esk4_0
@ ^ [Z0: $i,Z1: $i] : ( cHALF @ Z1 @ Z0 ) )
@ ( esk1_3 @ esk3_0 @ esk4_0
@ ^ [Z0: $i,Z1: $i] : ( cHALF @ Z1 @ Z0 ) ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_9]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO272^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.14 % Computer : n018.cluster.edu
% 0.08/0.14 % Model : x86_64 x86_64
% 0.08/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.14 % Memory : 8046.5625MB
% 0.08/0.14 % OS : Linux 6.8.0-71-generic
% 0.08/0.14 % CPULimit : 300
% 0.08/0.14 % WCLimit : 300
% 0.08/0.14 % DateTime : Tue Sep 29 16:44:41 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 Running higher-order theorem proving
% 0.08/0.19 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.L2Uz7qzrUE/E---3.1_323010.p
% 244.83/31.73 % Version: 3.5.1-ho
% 244.83/31.73 % Preprocessing class: HSSSSMSSSSSNSSA.
% 244.83/31.73 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 244.83/31.73 % Starting post_as_ho12 with 300s (1) cores
% 244.83/31.73 % Starting new_bool_9 with 300s (1) cores
% 244.83/31.73 % Starting post_as_ho1 with 300s (1) cores
% 244.83/31.73 % Starting post_as_ho4 with 300s (1) cores
% 244.83/31.73 % Starting post_as_ho2 with 300s (1) cores
% 244.83/31.73 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 244.83/31.73 % Starting full_lambda_10 with 300s (1) cores
% 244.83/31.73 % Starting new_ho_8 with 300s (1) cores
% 244.83/31.73 % post_as_ho12 with pid 323023 completed with status 0
% 244.83/31.73 % Result found by post_as_ho12
% 244.83/31.73 % Preprocessing class: HSSSSMSSSSSNSSA.
% 244.83/31.73 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 244.83/31.73 % Starting post_as_ho12 with 300s (1) cores
% 244.83/31.73 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 244.83/31.73 % No SInE strategy applied
% 244.83/31.73 % Search class: HGUNF-FFSS32-MSSFFSBN
% 244.83/31.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 244.83/31.73 % Starting SubtermCWHack with 31s (1) cores
% 244.83/31.73 % SubtermCWHack with pid 323032 completed with status 8
% 244.83/31.73 % Starting post_as_ho12 with 181s (1) cores
% 244.83/31.73 % post_as_ho12 with pid 323639 completed with status 0
% 244.83/31.73 % Result found by post_as_ho12
% 244.83/31.73 % Preprocessing class: HSSSSMSSSSSNSSA.
% 244.83/31.73 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 244.83/31.73 % Starting post_as_ho12 with 300s (1) cores
% 244.83/31.73 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 244.83/31.73 % No SInE strategy applied
% 244.83/31.73 % Search class: HGUNF-FFSS32-MSSFFSBN
% 244.83/31.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 244.83/31.73 % Starting SubtermCWHack with 31s (1) cores
% 244.83/31.73 % SubtermCWHack with pid 323032 completed with status 8
% 244.83/31.73 % Starting post_as_ho12 with 181s (1) cores
% 244.83/31.73 % Preprocessing time : 0.001 s
% 244.83/31.73 % Presaturation interreduction done
% 244.83/31.73
% 244.83/31.73 % Proof found!
% 244.83/31.73 % SZS status Theorem
% 244.83/31.73 % SZS output start CNFRefutation
% See solution above
% 244.83/31.73 % Parsed axioms : 5
% 244.83/31.73 % Removed by relevancy pruning/SinE : 0
% 244.83/31.73 % Initial clauses : 14
% 244.83/31.73 % Removed in clause preprocessing : 4
% 244.83/31.73 % Initial clauses in saturation : 10
% 244.83/31.73 % Processed clauses : 31
% 244.83/31.73 % ...of these trivial : 0
% 244.83/31.73 % ...subsumed : 0
% 244.83/31.73 % ...remaining for further processing : 30
% 244.83/31.73 % Other redundant clauses eliminated : 0
% 244.83/31.73 % Clauses deleted for lack of memory : 0
% 244.83/31.73 % Backward-subsumed : 0
% 244.83/31.73 % Backward-rewritten : 0
% 244.83/31.73 % Generated clauses : 55
% 244.83/31.73 % ...of the previous two non-redundant : 42
% 244.83/31.73 % ...aggressively subsumed : 0
% 244.83/31.73 % Contextual simplify-reflections : 0
% 244.83/31.73 % Paramodulations : 45
% 244.83/31.73 % Factorizations : 0
% 244.83/31.73 % NegExts : 0
% 244.83/31.73 % Equation resolutions : 4
% 244.83/31.73 % Disequality decompositions : 0
% 244.83/31.73 % Total rewrite steps : 6
% 244.83/31.73 % ...of those cached : 3
% 244.83/31.73 % Propositional unsat checks : 0
% 244.83/31.73 % Propositional check models : 0
% 244.83/31.73 % Propositional check unsatisfiable : 0
% 244.83/31.73 % Propositional clauses : 0
% 244.83/31.73 % Propositional clauses after purity: 0
% 244.83/31.73 % Propositional unsat core size : 0
% 244.83/31.73 % Propositional preprocessing time : 0.000
% 244.83/31.73 % Propositional encoding time : 0.000
% 244.83/31.73 % Propositional solver time : 0.000
% 244.83/31.73 % Success case prop preproc time : 0.000
% 244.83/31.73 % Success case prop encoding time : 0.000
% 244.83/31.73 % Success case prop solver time : 0.000
% 244.83/31.73 % Current number of processed clauses : 20
% 244.83/31.73 % Positive orientable unit clauses : 5
% 244.83/31.73 % Positive unorientable unit clauses: 0
% 244.83/31.73 % Negative unit clauses : 2
% 244.83/31.73 % Non-unit-clauses : 13
% 244.83/31.73 % Current number of unprocessed clauses: 31
% 244.83/31.73 % ...number of literals in the above : 82
% 244.83/31.73 % Current number of archived formulas : 0
% 244.83/31.73 % Current number of archived clauses : 10
% 244.83/31.73 % Clause-clause subsumption calls (NU) : 5
% 244.83/31.73 % Rec. Clause-clause subsumption calls : 5
% 244.83/31.73 % Non-unit clause-clause subsumptions : 0
% 244.83/31.73 % Unit Clause-clause subsumption calls : 1
% 244.83/31.73 % Rewrite failures with RHS unbound : 0
% 244.83/31.73 % BW rewrite match attempts : 0
% 244.83/31.73 % BW rewrite match successes : 0
% 244.83/31.73 % Condensation attempts : 0
% 244.83/31.73 % Condensation successes : 0
% 244.83/31.73 % Termbank termtop insertions : 10096
% 244.83/31.73 % Search garbage collected termcells : 365
% 244.83/31.73
% 244.83/31.73 % -------------------------------------------------
% 244.83/31.73 % User time : 30.449 s
% 244.83/31.73 % System time : 0.617 s
% 244.83/31.73 % Total time : 31.067 s
% 244.83/31.73 % Maximum resident set size: 3636 pages
% 244.83/31.73
% 244.83/31.73 % -------------------------------------------------
% 244.83/31.73 % User time : 30.451 s
% 244.83/31.73 % System time : 0.624 s
% 244.83/31.73 % Total time : 31.075 s
% 244.83/31.73 % Maximum resident set size: 4864 pages
% 244.83/31.73 % E exiting
%------------------------------------------------------------------------------