%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO222^5 : 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 : n001.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 08:42:35 AM UTC 2026
% Result : Theorem 0.26s 0.33s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 16 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 104 ( 14 ~; 14 |; 9 &; 61 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 2 ^; 23 !; 4 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
f: $i > $i ).
thf(decl_24,type,
a: $i ).
thf(decl_25,type,
cP: $i > $o ).
thf(decl_26,type,
esk1_1: ( $i > $o ) > $i ).
thf(cTHM115A,conjecture,
? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ ( f @ X2 ) )
=> ( cP @ X2 ) )
& ( ( ( cP @ a )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
= ( f @ X3 ) )
=> ( X2 = X3 ) ) )
=> ? [X4: $i] : ( X1 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MABRdi7S29/E---3.1_1481942.p',cTHM115A) ).
thf(c_0_1,negated_conjecture,
~ ? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ ( f @ X2 ) )
=> ( cP @ X2 ) )
& ( ( ( cP @ a )
& ! [X2: $i,X3: $i] :
( ( ( f @ X2 )
= ( f @ X3 ) )
=> ( X2 = X3 ) ) )
=> ? [X4: $i] : ( X1 @ X4 ) ) ),
inference(assume_negation,[status(cth)],[cTHM115A]) ).
thf(c_0_2,negated_conjecture,
! [X10: $i > $o,X12: $i,X13: $i,X14: $i] :
( ( ( cP @ a )
| ( X10 @ ( f @ ( esk1_1 @ X10 ) ) ) )
& ( ( ( f @ X12 )
!= ( f @ X13 ) )
| ( X12 = X13 )
| ( X10 @ ( f @ ( esk1_1 @ X10 ) ) ) )
& ( ~ ( X10 @ X14 )
| ( X10 @ ( f @ ( esk1_1 @ X10 ) ) ) )
& ( ( cP @ a )
| ~ ( cP @ ( esk1_1 @ X10 ) ) )
& ( ( ( f @ X12 )
!= ( f @ X13 ) )
| ( X12 = X13 )
| ~ ( cP @ ( esk1_1 @ X10 ) ) )
& ( ~ ( X10 @ X14 )
| ~ ( cP @ ( esk1_1 @ X10 ) ) ) ),
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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $i > $o,X2: $i,X3: $i] :
( ( X2 = X3 )
| ( X1 @ ( f @ ( esk1_1 @ X1 ) ) )
| ( ( f @ X2 )
!= ( f @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( f @ ( esk1_1 @ X1 ) ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( f @ X2 )
!= ( f @ X3 ) ) ),
inference(primitive_enumeration,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X2: $i] :
( ( f
@ ( esk1_1
@ ^ [Z0: $i] : ( Z0 = X2 ) ) )
= X2 ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i > $o] :
( ( cP @ a )
| ( X1 @ ( f @ ( esk1_1 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i,X1: $i > $o] :
( ~ ( X1 @ X2 )
| ~ ( cP @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i] :
( ( esk1_1
@ ^ [Z0: $i] :
( Z0
= ( f @ X2 ) ) )
= X2 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6])]) ).
thf(c_0_10,negated_conjecture,
cP @ a,
inference(primitive_enumeration,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i] :
~ ( cP @ X2 ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])])]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO222^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 % Computer : n001.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.22 % CPULimit : 300
% 0.07/0.22 % WCLimit : 300
% 0.07/0.22 % DateTime : Tue Sep 29 16:45:50 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running higher-order theorem proving
% 0.26/0.30 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.MABRdi7S29/E---3.1_1481942.p
% 0.26/0.33 % Version: 3.5.1-ho
% 0.26/0.33 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.26/0.33 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.33 % Starting post_as_ho12 with 300s (1) cores
% 0.26/0.33 % Starting new_bool_9 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho4 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho2 with 300s (1) cores
% 0.26/0.33 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.26/0.33 % Starting full_lambda_10 with 300s (1) cores
% 0.26/0.33 % Starting new_ho_8 with 300s (1) cores
% 0.26/0.33 % post_as_ho1 with pid 1481960 completed with status 0
% 0.26/0.33 % Result found by post_as_ho1
% 0.26/0.33 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.26/0.33 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.33 % Starting post_as_ho12 with 300s (1) cores
% 0.26/0.33 % Starting new_bool_9 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.33 % No SInE strategy applied
% 0.26/0.33 % Search class: HGHSF-FFSF11-SSSFFMBN
% 0.26/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.33 % SubtermCWHack with pid 1481967 completed with status 10
% 0.26/0.33 % Starting post_as_ho1 with 31s (1) cores
% 0.26/0.33 % post_as_ho1 with pid 1481976 completed with status 10
% 0.26/0.33 % Starting ehoh_best_sine_rwall with 28s (1) cores
% 0.26/0.33 % ehoh_best_sine_rwall with pid 1481984 completed with status 0
% 0.26/0.33 % Result found by ehoh_best_sine_rwall
% 0.26/0.33 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.26/0.33 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.33 % Starting post_as_ho12 with 300s (1) cores
% 0.26/0.33 % Starting new_bool_9 with 300s (1) cores
% 0.26/0.33 % Starting post_as_ho1 with 300s (1) cores
% 0.26/0.33 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.33 % No SInE strategy applied
% 0.26/0.33 % Search class: HGHSF-FFSF11-SSSFFMBN
% 0.26/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.26/0.33 % SubtermCWHack with pid 1481967 completed with status 10
% 0.26/0.33 % Starting post_as_ho1 with 31s (1) cores
% 0.26/0.33 % post_as_ho1 with pid 1481976 completed with status 10
% 0.26/0.33 % Starting ehoh_best_sine_rwall with 28s (1) cores
% 0.26/0.33 % Preprocessing time : 0.001 s
% 0.26/0.33 % Presaturation interreduction done
% 0.26/0.33
% 0.26/0.33 % Proof found!
% 0.26/0.33 % SZS status Theorem
% 0.26/0.33 % SZS output start CNFRefutation
% See solution above
% 0.26/0.33 % Parsed axioms : 4
% 0.26/0.33 % Removed by relevancy pruning/SinE : 0
% 0.26/0.33 % Initial clauses : 9
% 0.26/0.33 % Removed in clause preprocessing : 3
% 0.26/0.33 % Initial clauses in saturation : 6
% 0.26/0.33 % Processed clauses : 19
% 0.26/0.33 % ...of these trivial : 0
% 0.26/0.33 % ...subsumed : 0
% 0.26/0.33 % ...remaining for further processing : 19
% 0.26/0.33 % Other redundant clauses eliminated : 3
% 0.26/0.33 % Clauses deleted for lack of memory : 0
% 0.26/0.33 % Backward-subsumed : 5
% 0.26/0.33 % Backward-rewritten : 1
% 0.26/0.33 % Generated clauses : 35
% 0.26/0.33 % ...of the previous two non-redundant : 22
% 0.26/0.33 % ...aggressively subsumed : 0
% 0.26/0.33 % Contextual simplify-reflections : 0
% 0.26/0.33 % Paramodulations : 18
% 0.26/0.33 % Factorizations : 0
% 0.26/0.33 % NegExts : 0
% 0.26/0.33 % Equation resolutions : 5
% 0.26/0.33 % Disequality decompositions : 0
% 0.26/0.33 % Total rewrite steps : 2
% 0.26/0.33 % ...of those cached : 0
% 0.26/0.33 % Propositional unsat checks : 0
% 0.26/0.33 % Propositional check models : 0
% 0.26/0.33 % Propositional check unsatisfiable : 0
% 0.26/0.33 % Propositional clauses : 0
% 0.26/0.33 % Propositional clauses after purity: 0
% 0.26/0.33 % Propositional unsat core size : 0
% 0.26/0.33 % Propositional preprocessing time : 0.000
% 0.26/0.33 % Propositional encoding time : 0.000
% 0.26/0.33 % Propositional solver time : 0.000
% 0.26/0.33 % Success case prop preproc time : 0.000
% 0.26/0.33 % Success case prop encoding time : 0.000
% 0.26/0.33 % Success case prop solver time : 0.000
% 0.26/0.33 % Current number of processed clauses : 5
% 0.26/0.33 % Positive orientable unit clauses : 0
% 0.26/0.33 % Positive unorientable unit clauses: 2
% 0.26/0.33 % Negative unit clauses : 1
% 0.26/0.33 % Non-unit-clauses : 2
% 0.26/0.33 % Current number of unprocessed clauses: 13
% 0.26/0.33 % ...number of literals in the above : 20
% 0.26/0.33 % Current number of archived formulas : 0
% 0.26/0.33 % Current number of archived clauses : 14
% 0.26/0.33 % Clause-clause subsumption calls (NU) : 3
% 0.26/0.33 % Rec. Clause-clause subsumption calls : 3
% 0.26/0.33 % Non-unit clause-clause subsumptions : 2
% 0.26/0.33 % Unit Clause-clause subsumption calls : 5
% 0.26/0.33 % Rewrite failures with RHS unbound : 0
% 0.26/0.33 % BW rewrite match attempts : 31
% 0.26/0.33 % BW rewrite match successes : 17
% 0.26/0.33 % Condensation attempts : 0
% 0.26/0.33 % Condensation successes : 0
% 0.26/0.33 % Termbank termtop insertions : 1516
% 0.26/0.33 % Search garbage collected termcells : 139
% 0.26/0.33
% 0.26/0.33 % -------------------------------------------------
% 0.26/0.33 % User time : 0.009 s
% 0.26/0.33 % System time : 0.002 s
% 0.26/0.33 % Total time : 0.011 s
% 0.26/0.33 % Maximum resident set size: 3576 pages
% 0.26/0.33
% 0.26/0.33 % -------------------------------------------------
% 0.26/0.33 % User time : 0.009 s
% 0.26/0.33 % System time : 0.009 s
% 0.26/0.33 % Total time : 0.018 s
% 0.26/0.33 % Maximum resident set size: 4608 pages
% 0.26/0.33 % E exiting
%------------------------------------------------------------------------------