%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO537^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:44:48 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 117 ( 9 ~; 3 |; 1 &; 100 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 60 ( 27 ^; 12 !; 21 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(decl_24,type,
epsa: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(decl_25,type,
epsb: ( ( $i > $i ) > ( $i > $i ) > $o ) > $i > $i ).
thf(decl_26,type,
epred1_0: ( $i > $i ) > ( $i > $i ) > $o ).
thf(decl_27,type,
esk1_0: $i > $i ).
thf(decl_28,type,
esk2_0: $i > $i ).
thf(epsbd,axiom,
( epsb
= ( ^ [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [X4: $i > $i] : ( X3 @ ( epsa @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9ucLwhRqKX/E---3.1_3833791.p',epsbd) ).
thf(epsad,axiom,
( epsa
= ( ^ [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [X2: $i > $i] :
? [X4: $i > $i] : ( X3 @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9ucLwhRqKX/E---3.1_3833791.p',epsad) ).
thf(conj,conjecture,
! [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X2: $i > $i,X4: $i > $i] : ( X3 @ X2 @ X4 )
=> ( X3 @ ( epsa @ X3 ) @ ( epsb @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9ucLwhRqKX/E---3.1_3833791.p',conj) ).
thf(choiceaxii,axiom,
! [X1: ( $i > $i ) > $o] :
( ? [X2: $i > $i] : ( X1 @ X2 )
=> ( X1 @ ( epsii @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9ucLwhRqKX/E---3.1_3833791.p',choiceaxii) ).
thf(c_0_4,plain,
( epsb
= ( ^ [Z0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Z1: $i > $i] :
( Z0
@ ( epsii
@ ^ [Z2: $i > $i] :
? [X10: $i > $i] : ( Z0 @ Z2 @ X10 ) )
@ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[epsbd]) ).
thf(c_0_5,plain,
( epsa
= ( ^ [Z0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Z1: $i > $i] :
? [X4: $i > $i] : ( Z0 @ Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[epsad]) ).
thf(c_0_6,negated_conjecture,
~ ! [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X2: $i > $i,X4: $i > $i] : ( X3 @ X2 @ X4 )
=> ( X3 @ ( epsa @ X3 ) @ ( epsb @ X3 ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_7,plain,
( epsb
= ( ^ [Z0: ( $i > $i ) > ( $i > $i ) > $o] :
( epsii
@ ^ [Z1: $i > $i] :
( Z0
@ ( epsii
@ ^ [Z2: $i > $i] :
? [X10: $i > $i] : ( Z0 @ Z2 @ X10 ) )
@ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ! [X3: ( $i > $i ) > ( $i > $i ) > $o] :
( ? [X2: $i > $i,X4: $i > $i] : ( X3 @ X2 @ X4 )
=> ( X3
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X11: $i > $i] : ( X3 @ Z0 @ X11 ) )
@ ( epsii
@ ^ [Z0: $i > $i] :
( X3
@ ( epsii
@ ^ [Z1: $i > $i] :
? [X12: $i > $i] : ( X3 @ Z1 @ X12 ) )
@ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_5]),c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
& ~ ( epred1_0
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X11: $i > $i] : ( epred1_0 @ Z0 @ X11 ) )
@ ( epsii
@ ( epred1_0
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X12: $i > $i] : ( epred1_0 @ Z0 @ X12 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
thf(c_0_10,plain,
! [X16: ( $i > $i ) > $o,X17: $i > $i] :
( ~ ( X16 @ X17 )
| ( X16 @ ( epsii @ X16 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxii])])])]) ).
thf(c_0_11,negated_conjecture,
~ ( epred1_0
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X24: $i > $i] :
( epred1_0 @ Z0
@ ^ [Z1: $i] : ( X24 @ Z1 ) ) )
@ ( epsii
@ ( epred1_0
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X25: $i > $i] :
( epred1_0 @ Z0
@ ^ [Z1: $i] : ( X25 @ Z1 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ ( epsii @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i > $i] :
( ? [X26: $i > $i] :
( epred1_0
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X27: $i > $i] :
( epred1_0 @ Z0
@ ^ [Z1: $i] : ( X27 @ Z1 ) ) )
@ ^ [Z0: $i] : ( X26 @ Z0 ) )
| ~ ? [X28: $i > $i] :
( epred1_0 @ X2
@ ^ [Z0: $i] : ( X28 @ Z0 ) ) ),
inference(choice_inst,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i > $i] :
~ ( epred1_0
@ ( epsii
@ ^ [Z0: $i > $i] :
? [X29: $i > $i] :
( epred1_0 @ Z0
@ ^ [Z1: $i] : ( X29 @ Z1 ) ) )
@ X2 ),
inference(sr,[status(thm)],[inference(choice_inst,[status(thm)],[c_0_11,c_0_12]),c_0_11]) ).
thf(c_0_15,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i > $i,X4: $i > $i] :
~ ( epred1_0 @ X2 @ X4 ),
inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_13]),c_0_14]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_15,c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO537^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:17:03 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.9ucLwhRqKX/E---3.1_3833791.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSMCHHA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.26 % ehoh_best_sine_rwall with pid 3833805 completed with status 0
% 0.08/0.26 % Result found by ehoh_best_sine_rwall
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSMCHHA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.26 % Search class: HHUNF-FFSF22-DHHFFSBC
% 0.08/0.26 % partial match(3): HGUNF-FFSF22-SHHFFSBN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 3833809 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSSSMCHHA.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.08/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.08/0.26 % Search class: HHUNF-FFSF22-DHHFFSBC
% 0.08/0.26 % partial match(3): HGUNF-FFSF22-SHHFFSBN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 7
% 0.08/0.26 % Removed by relevancy pruning/SinE : 3
% 0.08/0.26 % Initial clauses : 3
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 3
% 0.08/0.26 % Processed clauses : 8
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 8
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 3
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 13
% 0.08/0.26 % ...of the previous two non-redundant : 9
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 2
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 2
% 0.08/0.26 % ...of those cached : 1
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 2
% 0.08/0.26 % Positive orientable unit clauses : 0
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 1
% 0.08/0.26 % Current number of unprocessed clauses: 4
% 0.08/0.26 % ...number of literals in the above : 8
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 6
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 1
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 1
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 3
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 2093
% 0.08/0.26 % Search garbage collected termcells : 172
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.004 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.005 s
% 0.08/0.26 % Maximum resident set size: 3636 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.004 s
% 0.08/0.26 % System time : 0.007 s
% 0.08/0.26 % Total time : 0.011 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------