%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO543^1 : 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 08:43:23 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 24 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 69 ( 16 ~; 12 |; 18 &; 22 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 26 ( 13 ^; 12 !; 1 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(decl_24,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_25,type,
epred1_0: $o ).
thf(decl_26,type,
esk1_0: $i > $i ).
thf(conj,conjecture,
! [X3: $o,X2: $i > $i] :
( ( if @ X3 @ X2 @ X2 )
= X2 ),
file('/export/starexec/sandbox/tmp/tmp.PiDuIgjKjN/E---3.1_3834661.p',conj) ).
thf(ifd,axiom,
( if
= ( ^ [X3: $o,X2: $i > $i,X4: $i > $i] :
( epsii
@ ^ [X5: $i > $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PiDuIgjKjN/E---3.1_3834661.p',ifd) ).
thf(choiceaxii,axiom,
! [X1: ( $i > $i ) > $o] :
( ? [X2: $i > $i] : ( X1 @ X2 )
=> ( X1 @ ( epsii @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PiDuIgjKjN/E---3.1_3834661.p',choiceaxii) ).
thf(c_0_3,negated_conjecture,
~ ! [X3: $o,X2: $i > $i] :
( ( if @ X3 @ X2 @ X2 )
= X2 ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_4,plain,
( if
= ( ^ [Z0: $o,Z1: $i > $i,Z2: $i > $i] :
( epsii
@ ^ [Z3: $i > $i] :
( ( Z0
& ( Z3 = Z1 ) )
| ( ~ Z0
& Z3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifd]) ).
thf(c_0_5,negated_conjecture,
~ ! [X3: $o,X2: $i > $i] :
( ( epsii
@ ^ [Z0: $i > $i] :
( ( X3
& ( Z0 = X2 ) )
| ( ~ X3
& ( Z0 = X2 ) ) ) )
= X2 ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk1_0 ) ) ) )
!= esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_7,plain,
! [X12: ( $i > $i ) > $o,X13: $i > $i] :
( ~ ( X12 @ X13 )
| ( X12 @ ( epsii @ X12 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceaxii])])])]) ).
thf(c_0_8,negated_conjecture,
( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk1_0 ) ) ) )
!= esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: ( $i > $i ) > $o,X2: $i > $i] :
( ( X1 @ ( epsii @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i > $i] :
( ( epred1_0
& ( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk1_0 ) ) ) )
= esk1_0 ) )
| ( ~ epred1_0
& ( ( epsii
@ ^ [Z0: $i > $i] :
( ( epred1_0
& ( Z0 = esk1_0 ) )
| ( ~ epred1_0
& ( Z0 = esk1_0 ) ) ) )
= esk1_0 ) )
| ~ ( ( epred1_0
& ( X2 = esk1_0 ) )
| ( ~ epred1_0
& ( X2 = esk1_0 ) ) ) ),
inference(choice_inst,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
epred1_0,
inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10])]),c_0_8])]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10])]),c_0_8])]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO543^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n015.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 17:17:32 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 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.PiDuIgjKjN/E---3.1_3834661.p
% 0.10/0.23 % Version: 3.5.1-ho
% 0.10/0.23 % Preprocessing class: HSSSSMSSSSSCHSA.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.23 % Starting sh5l with 300s (1) cores
% 0.10/0.23 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.23 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.23 % sh5l with pid 3834675 completed with status 0
% 0.10/0.23 % Result found by sh5l
% 0.10/0.23 % Preprocessing class: HSSSSMSSSSSCHSA.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.23 % Starting sh5l with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.23 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.23 % Search class: HHUSF-FFSF22-MHSFFMBC
% 0.10/0.23 % partial match(3): HHUSS-FFSF21-MHHFFMBC
% 0.10/0.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.23 % SubtermCWHack with pid 3834683 completed with status 0
% 0.10/0.23 % Result found by SubtermCWHack
% 0.10/0.23 % Preprocessing class: HSSSSMSSSSSCHSA.
% 0.10/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.23 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.23 % Starting sh5l with 300s (1) cores
% 0.10/0.23 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.23 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.23 % Search class: HHUSF-FFSF22-MHSFFMBC
% 0.10/0.23 % partial match(3): HHUSS-FFSF21-MHHFFMBC
% 0.10/0.23 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.23 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.23 % Preprocessing time : 0.001 s
% 0.10/0.23
% 0.10/0.23 % Proof found!
% 0.10/0.23 % SZS status Theorem
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.23 % Parsed axioms : 5
% 0.10/0.23 % Removed by relevancy pruning/SinE : 2
% 0.10/0.23 % Initial clauses : 2
% 0.10/0.23 % Removed in clause preprocessing : 0
% 0.10/0.23 % Initial clauses in saturation : 2
% 0.10/0.23 % Processed clauses : 5
% 0.10/0.23 % ...of these trivial : 0
% 0.10/0.23 % ...subsumed : 0
% 0.10/0.23 % ...remaining for further processing : 4
% 0.10/0.23 % Other redundant clauses eliminated : 4
% 0.10/0.23 % Clauses deleted for lack of memory : 0
% 0.10/0.23 % Backward-subsumed : 0
% 0.10/0.23 % Backward-rewritten : 0
% 0.10/0.23 % Generated clauses : 14
% 0.10/0.23 % ...of the previous two non-redundant : 6
% 0.10/0.23 % ...aggressively subsumed : 0
% 0.10/0.23 % Contextual simplify-reflections : 0
% 0.10/0.23 % Paramodulations : 0
% 0.10/0.23 % Factorizations : 0
% 0.10/0.23 % NegExts : 0
% 0.10/0.23 % Equation resolutions : 4
% 0.10/0.23 % Disequality decompositions : 0
% 0.10/0.23 % Total rewrite steps : 1
% 0.10/0.23 % ...of those cached : 0
% 0.10/0.23 % Propositional unsat checks : 0
% 0.10/0.23 % Propositional check models : 0
% 0.10/0.23 % Propositional check unsatisfiable : 0
% 0.10/0.23 % Propositional clauses : 0
% 0.10/0.23 % Propositional clauses after purity: 0
% 0.10/0.23 % Propositional unsat core size : 0
% 0.10/0.23 % Propositional preprocessing time : 0.000
% 0.10/0.23 % Propositional encoding time : 0.000
% 0.10/0.23 % Propositional solver time : 0.000
% 0.10/0.23 % Success case prop preproc time : 0.000
% 0.10/0.23 % Success case prop encoding time : 0.000
% 0.10/0.23 % Success case prop solver time : 0.000
% 0.10/0.23 % Current number of processed clauses : 3
% 0.10/0.23 % Positive orientable unit clauses : 1
% 0.10/0.23 % Positive unorientable unit clauses: 0
% 0.10/0.23 % Negative unit clauses : 1
% 0.10/0.23 % Non-unit-clauses : 1
% 0.10/0.23 % Current number of unprocessed clauses: 3
% 0.10/0.23 % ...number of literals in the above : 4
% 0.10/0.23 % Current number of archived formulas : 0
% 0.10/0.23 % Current number of archived clauses : 1
% 0.10/0.23 % Clause-clause subsumption calls (NU) : 1
% 0.10/0.23 % Rec. Clause-clause subsumption calls : 1
% 0.10/0.23 % Non-unit clause-clause subsumptions : 0
% 0.10/0.23 % Unit Clause-clause subsumption calls : 1
% 0.10/0.23 % Rewrite failures with RHS unbound : 0
% 0.10/0.23 % BW rewrite match attempts : 0
% 0.10/0.23 % BW rewrite match successes : 0
% 0.10/0.23 % Condensation attempts : 0
% 0.10/0.23 % Condensation successes : 0
% 0.10/0.23 % Termbank termtop insertions : 1779
% 0.10/0.23 % Search garbage collected termcells : 68
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.003 s
% 0.10/0.23 % System time : 0.002 s
% 0.10/0.23 % Total time : 0.006 s
% 0.10/0.23 % Maximum resident set size: 3892 pages
% 0.10/0.23
% 0.10/0.23 % -------------------------------------------------
% 0.10/0.23 % User time : 0.004 s
% 0.10/0.23 % System time : 0.007 s
% 0.10/0.23 % Total time : 0.011 s
% 0.10/0.23 % Maximum resident set size: 4864 pages
% 0.10/0.23 % E exiting
%------------------------------------------------------------------------------