%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN365^5 : 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 : n010.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 08:41:02 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 0 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 124 ( 16 ~; 10 |; 13 &; 77 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 14 !; 4 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cP: $i > $o ).
thf(decl_24,type,
cR: $i > $i > $o ).
thf(decl_25,type,
h: $i > $i ).
thf(decl_26,type,
g: $i > $i ).
thf(decl_27,type,
esk1_1: $i > $i ).
thf(decl_28,type,
esk2_0: $i ).
thf(cX2116,conjecture,
( ( ! [X1: $i] :
? [X2: $i] :
( ( cP @ X1 )
=> ( ( cR @ X1 @ ( g @ ( h @ X2 ) ) )
& ( cP @ X2 ) ) )
& ! [X3: $i] :
( ( cP @ X3 )
=> ( ( cP @ ( g @ X3 ) )
& ( cP @ ( h @ X3 ) ) ) ) )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ? [X2: $i] :
( ( cR @ X1 @ X2 )
& ( cP @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NRix6iAfAC/E---3.1_3063003.p',cX2116) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $i] :
? [X2: $i] :
( ( cP @ X1 )
=> ( ( cR @ X1 @ ( g @ ( h @ X2 ) ) )
& ( cP @ X2 ) ) )
& ! [X3: $i] :
( ( cP @ X3 )
=> ( ( cP @ ( g @ X3 ) )
& ( cP @ ( h @ X3 ) ) ) ) )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ? [X2: $i] :
( ( cR @ X1 @ X2 )
& ( cP @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cX2116]) ).
thf(c_0_2,negated_conjecture,
! [X9: $i,X11: $i,X13: $i] :
( ( ( cR @ X9 @ ( g @ ( h @ ( esk1_1 @ X9 ) ) ) )
| ~ ( cP @ X9 ) )
& ( ( cP @ ( esk1_1 @ X9 ) )
| ~ ( cP @ X9 ) )
& ( ( cP @ ( g @ X11 ) )
| ~ ( cP @ X11 ) )
& ( ( cP @ ( h @ X11 ) )
| ~ ( cP @ X11 ) )
& ( cP @ esk2_0 )
& ( ~ ( cR @ esk2_0 @ X13 )
| ~ ( cP @ X13 ) ) ),
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] :
( ~ ( cR @ esk2_0 @ X1 )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i] :
( ( cR @ X1 @ ( g @ ( h @ ( esk1_1 @ X1 ) ) ) )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
cP @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
~ ( cP @ ( g @ ( h @ ( esk1_1 @ esk2_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_5])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( cP @ ( g @ X1 ) )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
~ ( cP @ ( h @ ( esk1_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ( cP @ ( h @ X1 ) )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_10,negated_conjecture,
~ ( cP @ ( esk1_1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( cP @ ( esk1_1 @ X1 ) )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_5])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN365^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:15:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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.NRix6iAfAC/E---3.1_3063003.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % Starting sh4l with 300s (1) cores
% 0.22/0.27 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.22/0.27 % ho_unfolding_6 with pid 3063017 completed with status 0
% 0.22/0.27 % Result found by ho_unfolding_6
% 0.22/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HHHNF-FFSF11-MFFFFFNN
% 0.22/0.27 % partial match(1): FHHNF-FFSF11-MFFFFFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 3063020 completed with status 0
% 0.22/0.27 % Result found by SubtermCWHack
% 0.22/0.27 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.22/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HHHNF-FFSF11-MFFFFFNN
% 0.22/0.27 % partial match(1): FHHNF-FFSF11-MFFFFFNN
% 0.22/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.27 % Preprocessing time : 0.001 s
% 0.22/0.27
% 0.22/0.27 % Proof found!
% 0.22/0.27 % SZS status Theorem
% 0.22/0.27 % SZS output start CNFRefutation
% See solution above
% 0.22/0.27 % Parsed axioms : 5
% 0.22/0.27 % Removed by relevancy pruning/SinE : 0
% 0.22/0.27 % Initial clauses : 10
% 0.22/0.27 % Removed in clause preprocessing : 4
% 0.22/0.27 % Initial clauses in saturation : 6
% 0.22/0.27 % Processed clauses : 9
% 0.22/0.27 % ...of these trivial : 0
% 0.22/0.27 % ...subsumed : 0
% 0.22/0.27 % ...remaining for further processing : 9
% 0.22/0.27 % Other redundant clauses eliminated : 0
% 0.22/0.27 % Clauses deleted for lack of memory : 0
% 0.22/0.27 % Backward-subsumed : 0
% 0.22/0.27 % Backward-rewritten : 0
% 0.22/0.27 % Generated clauses : 4
% 0.22/0.27 % ...of the previous two non-redundant : 3
% 0.22/0.27 % ...aggressively subsumed : 0
% 0.22/0.27 % Contextual simplify-reflections : 0
% 0.22/0.27 % Paramodulations : 4
% 0.22/0.27 % Factorizations : 0
% 0.22/0.27 % NegExts : 0
% 0.22/0.27 % Equation resolutions : 0
% 0.22/0.27 % Disequality decompositions : 0
% 0.22/0.27 % Total rewrite steps : 2
% 0.22/0.27 % ...of those cached : 1
% 0.22/0.27 % Propositional unsat checks : 0
% 0.22/0.27 % Propositional check models : 0
% 0.22/0.27 % Propositional check unsatisfiable : 0
% 0.22/0.27 % Propositional clauses : 0
% 0.22/0.27 % Propositional clauses after purity: 0
% 0.22/0.27 % Propositional unsat core size : 0
% 0.22/0.27 % Propositional preprocessing time : 0.000
% 0.22/0.27 % Propositional encoding time : 0.000
% 0.22/0.27 % Propositional solver time : 0.000
% 0.22/0.27 % Success case prop preproc time : 0.000
% 0.22/0.27 % Success case prop encoding time : 0.000
% 0.22/0.27 % Success case prop solver time : 0.000
% 0.22/0.27 % Current number of processed clauses : 9
% 0.22/0.27 % Positive orientable unit clauses : 1
% 0.22/0.27 % Positive unorientable unit clauses: 0
% 0.22/0.27 % Negative unit clauses : 3
% 0.22/0.27 % Non-unit-clauses : 5
% 0.22/0.27 % Current number of unprocessed clauses: 0
% 0.22/0.27 % ...number of literals in the above : 0
% 0.22/0.27 % Current number of archived formulas : 0
% 0.22/0.27 % Current number of archived clauses : 0
% 0.22/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.27 % Non-unit clause-clause subsumptions : 0
% 0.22/0.27 % Unit Clause-clause subsumption calls : 6
% 0.22/0.27 % Rewrite failures with RHS unbound : 0
% 0.22/0.27 % BW rewrite match attempts : 0
% 0.22/0.27 % BW rewrite match successes : 0
% 0.22/0.27 % Condensation attempts : 0
% 0.22/0.27 % Condensation successes : 0
% 0.22/0.27 % Termbank termtop insertions : 587
% 0.22/0.27 % Search garbage collected termcells : 187
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.001 s
% 0.22/0.27 % System time : 0.004 s
% 0.22/0.27 % Total time : 0.004 s
% 0.22/0.27 % Maximum resident set size: 3628 pages
% 0.22/0.27
% 0.22/0.27 % -------------------------------------------------
% 0.22/0.27 % User time : 0.001 s
% 0.22/0.27 % System time : 0.009 s
% 0.22/0.27 % Total time : 0.010 s
% 0.22/0.27 % Maximum resident set size: 4864 pages
% 0.22/0.27 % E exiting
%------------------------------------------------------------------------------