%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:42:09 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 258 ( 0 equ; 0 cnn)
% Maximal formula atoms : 154 ( 14 avg)
% Number of connectives : 427 ( 95 ~; 109 |; 40 &; 180 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 4 ^; 0 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
f: $o > $i > $i ).
thf(decl_24,type,
p: ( $i > $i ) > $o ).
thf(decl_25,type,
a: ( $i > $i ) > $o ).
thf(decl_26,type,
b: $o ).
thf(conj,conjecture,
( ( p
@ ^ [X1: $i] :
( f
@ ( ( a
@ ^ [X1: $i] : ( f @ b @ X1 ) )
& b )
@ X1 ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eUi0t1TDG3/E---3.1_1870814.p',conj) ).
thf(c_0_1,negated_conjecture,
~ ( ( p
@ ^ [X1: $i] :
( f
@ ( ( a
@ ^ [X1: $i] : ( f @ b @ X1 ) )
& b )
@ X1 ) )
=> ( p
@ ( f
@ ( b
& ( a @ ( f @ b ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ( ~ ( ( ~ b
| ( a @ ( f @ $true ) ) )
& ( b
| ( a @ ( f @ $false ) ) )
& b )
| ( p @ ( f @ $true ) ) )
& ( ( ( ~ b
| ( a @ ( f @ $true ) ) )
& ( b
| ( a @ ( f @ $false ) ) )
& b )
| ( p @ ( f @ $false ) ) ) )
=> ( ( ~ ( b
& ( ~ b
| ( a @ ( f @ $true ) ) )
& ( b
| ( a @ ( f @ $false ) ) ) )
| ( p @ ( f @ $true ) ) )
& ( ( b
& ( ~ b
| ( a @ ( f @ $true ) ) )
& ( b
| ( a @ ( f @ $false ) ) ) )
| ( p @ ( f @ $false ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
( ( ~ b
| b
| ~ b
| ( p @ ( f @ $true ) ) )
& ( ~ ( a @ ( f @ $false ) )
| b
| ~ b
| ( p @ ( f @ $true ) ) )
& ( ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b
| ( p @ ( f @ $true ) ) )
& ( ~ ( a @ ( f @ $false ) )
| ~ ( a @ ( f @ $true ) )
| ~ b
| ( p @ ( f @ $true ) ) )
& ( ~ b
| ( a @ ( f @ $true ) )
| ( p @ ( f @ $false ) ) )
& ( b
| ( a @ ( f @ $false ) )
| ( p @ ( f @ $false ) ) )
& ( b
| ( p @ ( f @ $false ) ) )
& ( ~ b
| b
| ~ b
| b )
& ( ~ ( a @ ( f @ $false ) )
| b
| ~ b
| b )
& ( ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b
| b )
& ( ~ ( a @ ( f @ $false ) )
| ~ ( a @ ( f @ $true ) )
| ~ b
| b )
& ( ~ ( p @ ( f @ $false ) )
| b )
& ( ~ b
| b
| ~ b
| ~ b
| ( a @ ( f @ $true ) ) )
& ( ~ ( a @ ( f @ $false ) )
| b
| ~ b
| ~ b
| ( a @ ( f @ $true ) ) )
& ( ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b
| ~ b
| ( a @ ( f @ $true ) ) )
& ( ~ ( a @ ( f @ $false ) )
| ~ ( a @ ( f @ $true ) )
| ~ b
| ~ b
| ( a @ ( f @ $true ) ) )
& ( ~ ( p @ ( f @ $false ) )
| ~ b
| ( a @ ( f @ $true ) ) )
& ( ~ b
| b
| ~ b
| b
| ( a @ ( f @ $false ) ) )
& ( ~ ( a @ ( f @ $false ) )
| b
| ~ b
| b
| ( a @ ( f @ $false ) ) )
& ( ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b
| b
| ( a @ ( f @ $false ) ) )
& ( ~ ( a @ ( f @ $false ) )
| ~ ( a @ ( f @ $true ) )
| ~ b
| b
| ( a @ ( f @ $false ) ) )
& ( ~ ( p @ ( f @ $false ) )
| b
| ( a @ ( f @ $false ) ) )
& ( ~ b
| b
| ~ b
| ~ ( p @ ( f @ $true ) ) )
& ( ~ ( a @ ( f @ $false ) )
| b
| ~ b
| ~ ( p @ ( f @ $true ) ) )
& ( ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b
| ~ ( p @ ( f @ $true ) ) )
& ( ~ ( a @ ( f @ $false ) )
| ~ ( a @ ( f @ $true ) )
| ~ b
| ~ ( p @ ( f @ $true ) ) )
& ( ~ ( p @ ( f @ $false ) )
| ~ ( p @ ( f @ $true ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
thf(c_0_4,negated_conjecture,
( b
| ~ ( p @ ( f @ ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( b
| ( p @ ( f @ ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
( ( p @ ( f @ $true ) )
| ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
( ( a @ ( f @ $true ) )
| ( p @ ( f @ ~ $true ) )
| ~ b ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
b,
inference(csr,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ( p @ ( f @ $true ) )
| ~ b
| ~ ( a @ ( f @ $true ) ) ),
inference(cn,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( a @ ( f @ $true ) )
| ~ ( p @ ( f @ ~ $true ) )
| ~ b ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_11,negated_conjecture,
( ( p @ ( f @ ~ $true ) )
| ( a @ ( f @ $true ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]) ).
thf(c_0_12,negated_conjecture,
( ~ b
| ~ ( a @ ( f @ $true ) )
| ~ b
| ~ ( p @ ( f @ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_13,negated_conjecture,
( ( p @ ( f @ $true ) )
| ~ ( a @ ( f @ $true ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_8])]) ).
thf(c_0_14,negated_conjecture,
a @ ( f @ $true ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_8])]),c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ~ b
| ~ ( p @ ( f @ $true ) )
| ~ ( a @ ( f @ $true ) ) ),
inference(cn,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
p @ ( f @ $true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_8]),c_0_16]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO018^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n005.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:22:20 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 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.eUi0t1TDG3/E---3.1_1870814.p
% 0.10/0.25 % Version: 3.5.1-ho
% 0.10/0.25 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting sh3 with 1500s (5) cores
% 0.10/0.25 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.10/0.25 % Starting sh2lt with 300s (1) cores
% 0.10/0.25 % Starting ho_unfolding_1 with 300s (1) cores
% 0.10/0.25 % ho_unfolding_1 with pid 1870853 completed with status 0
% 0.10/0.25 % Result found by ho_unfolding_1
% 0.10/0.25 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting sh3 with 1500s (5) cores
% 0.10/0.25 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.10/0.25 % Starting sh2lt with 300s (1) cores
% 0.10/0.25 % Starting ho_unfolding_1 with 300s (1) cores
% 0.10/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HGHNF-FFSF22-SSSFFFNN
% 0.10/0.25 % partial match(2): HGHNF-FFSF00-SSSFFFNN
% 0.10/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.25 % SubtermCWHack with pid 1870854 completed with status 0
% 0.10/0.25 % Result found by SubtermCWHack
% 0.10/0.25 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting sh3 with 1500s (5) cores
% 0.10/0.25 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.10/0.25 % Starting sh2lt with 300s (1) cores
% 0.10/0.25 % Starting ho_unfolding_1 with 300s (1) cores
% 0.10/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HGHNF-FFSF22-SSSFFFNN
% 0.10/0.25 % partial match(2): HGHNF-FFSF00-SSSFFFNN
% 0.10/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.25 % Preprocessing time : 0.001 s
% 0.10/0.25
% 0.10/0.25 % Proof found!
% 0.10/0.25 % SZS status Theorem
% 0.10/0.25 % SZS output start CNFRefutation
% See solution above
% 0.10/0.25 % Parsed axioms : 5
% 0.10/0.25 % Removed by relevancy pruning/SinE : 0
% 0.10/0.25 % Initial clauses : 31
% 0.10/0.25 % Removed in clause preprocessing : 20
% 0.10/0.25 % Initial clauses in saturation : 11
% 0.10/0.25 % Processed clauses : 11
% 0.10/0.25 % ...of these trivial : 2
% 0.10/0.25 % ...subsumed : 0
% 0.10/0.25 % ...remaining for further processing : 8
% 0.10/0.25 % Other redundant clauses eliminated : 0
% 0.10/0.25 % Clauses deleted for lack of memory : 0
% 0.10/0.25 % Backward-subsumed : 1
% 0.10/0.25 % Backward-rewritten : 4
% 0.10/0.25 % Generated clauses : 2
% 0.10/0.25 % ...of the previous two non-redundant : 3
% 0.10/0.25 % ...aggressively subsumed : 0
% 0.10/0.25 % Contextual simplify-reflections : 2
% 0.10/0.25 % Paramodulations : 2
% 0.10/0.25 % Factorizations : 0
% 0.10/0.25 % NegExts : 0
% 0.10/0.25 % Equation resolutions : 0
% 0.10/0.25 % Disequality decompositions : 0
% 0.10/0.25 % Total rewrite steps : 12
% 0.10/0.25 % ...of those cached : 9
% 0.10/0.25 % Propositional unsat checks : 0
% 0.10/0.25 % Propositional check models : 0
% 0.10/0.25 % Propositional check unsatisfiable : 0
% 0.10/0.25 % Propositional clauses : 0
% 0.10/0.25 % Propositional clauses after purity: 0
% 0.10/0.25 % Propositional unsat core size : 0
% 0.10/0.25 % Propositional preprocessing time : 0.000
% 0.10/0.25 % Propositional encoding time : 0.000
% 0.10/0.25 % Propositional solver time : 0.000
% 0.10/0.25 % Success case prop preproc time : 0.000
% 0.10/0.25 % Success case prop encoding time : 0.000
% 0.10/0.25 % Success case prop solver time : 0.000
% 0.10/0.25 % Current number of processed clauses : 3
% 0.10/0.25 % Positive orientable unit clauses : 3
% 0.10/0.25 % Positive unorientable unit clauses: 0
% 0.10/0.25 % Negative unit clauses : 0
% 0.10/0.25 % Non-unit-clauses : 0
% 0.10/0.25 % Current number of unprocessed clauses: 3
% 0.10/0.25 % ...number of literals in the above : 9
% 0.10/0.25 % Current number of archived formulas : 0
% 0.10/0.25 % Current number of archived clauses : 5
% 0.10/0.25 % Clause-clause subsumption calls (NU) : 2
% 0.10/0.25 % Rec. Clause-clause subsumption calls : 2
% 0.10/0.25 % Non-unit clause-clause subsumptions : 2
% 0.10/0.25 % Unit Clause-clause subsumption calls : 1
% 0.10/0.25 % Rewrite failures with RHS unbound : 0
% 0.10/0.25 % BW rewrite match attempts : 3
% 0.10/0.25 % BW rewrite match successes : 3
% 0.10/0.25 % Condensation attempts : 0
% 0.10/0.25 % Condensation successes : 0
% 0.10/0.25 % Termbank termtop insertions : 1343
% 0.10/0.25 % Search garbage collected termcells : 159
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.004 s
% 0.10/0.25 % System time : 0.000 s
% 0.10/0.25 % Total time : 0.005 s
% 0.10/0.25 % Maximum resident set size: 3564 pages
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.006 s
% 0.10/0.25 % System time : 0.005 s
% 0.10/0.25 % Total time : 0.011 s
% 0.10/0.25 % Maximum resident set size: 4864 pages
% 0.10/0.25 % E exiting
%------------------------------------------------------------------------------