%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO538^1 : 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 : n009.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 08:43:22 AM UTC 2026
% Result : Theorem 0.25s 0.29s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 35 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 92 ( 26 ~; 13 |; 19 &; 33 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-3 aty)
% Number of variables : 30 ( 18 ^; 11 !; 1 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
eps: ( $i > $o ) > $i ).
thf(decl_24,type,
if: $o > $i > $i > $i ).
thf(decl_25,type,
esk1_0: $i ).
thf(decl_26,type,
esk2_0: $i ).
thf(conj,conjecture,
! [X2: $i,X4: $i] :
( ( ( if @ $true @ X2 @ X4 )
= X2 )
& ( ( if @ ~ $true @ X2 @ X4 )
= X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.dHSNWPRD9Q/E---3.1_95949.p',conj) ).
thf(ifd,axiom,
( if
= ( ^ [X3: $o,X2: $i,X4: $i] :
( eps
@ ^ [X5: $i] :
( ( X3
& ( X5 = X2 ) )
| ( ~ X3
& ( X5 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dHSNWPRD9Q/E---3.1_95949.p',ifd) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dHSNWPRD9Q/E---3.1_95949.p',choiceax) ).
thf(c_0_3,negated_conjecture,
~ ! [X2: $i,X4: $i] :
( ( ( if @ $true @ X2 @ X4 )
= X2 )
& ( ( if @ ~ $true @ X2 @ X4 )
= X4 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_4,plain,
( if
= ( ^ [Z0: $o,Z1: $i,Z2: $i] :
( eps
@ ^ [Z3: $i] :
( ( Z0
& ( Z3 = Z1 ) )
| ( ~ Z0
& Z3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ifd]) ).
thf(c_0_5,negated_conjecture,
~ ! [X2: $i,X4: $i] :
( ( ( eps
@ ^ [Z0: $i] :
( ( $true
& ( Z0 = X2 ) )
| ( ~ $true
& ( Z0 = X4 ) ) ) )
= X2 )
& ( ( eps
@ ^ [Z0: $i] :
( ( ~ $true
& ( Z0 = X2 ) )
| ( ~ ~ $true
& ( Z0 = X4 ) ) ) )
= X4 ) ),
inference(apply_def,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
( ( ( eps
@ ^ [Z0: $i] :
( ( $true
& ( Z0 = esk1_0 ) )
| ( ~ $true
& ( Z0 = esk2_0 ) ) ) )
!= esk1_0 )
| ( ( eps
@ ^ [Z0: $i] :
( ( ~ $true
& ( Z0 = esk1_0 ) )
| ( ~ ~ $true
& ( Z0 = esk2_0 ) ) ) )
!= esk2_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,negated_conjecture,
( ( ( eps
@ ^ [Z0: $i] :
( ( $true
& ( Z0 = esk1_0 ) )
| ( ~ $true
& ( Z0 = esk2_0 ) ) ) )
!= esk1_0 )
| ( ( eps
@ ^ [Z0: $i] :
( ( ~ $true
& ( Z0 = esk1_0 ) )
| ( ~ ~ $true
& ( Z0 = esk2_0 ) ) ) )
!= esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
! [X10: $i > $o,X11: $i] :
( ~ ( X10 @ X11 )
| ( X10 @ ( eps @ X10 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])]) ).
thf(c_0_9,negated_conjecture,
( ( ( eps
@ ^ [Z0: $i] : ( Z0 = esk1_0 ) )
!= esk1_0 )
| ( ( eps
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
!= esk2_0 ) ),
inference(cn,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( eps @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
( ( eps
@ ^ [Z0: $i] : ( Z0 = esk1_0 ) )
= esk1_0 ),
inference(er,[status(thm)],[inference(choice_inst,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9,c_0_10])]) ).
thf(c_0_12,negated_conjecture,
( ( eps
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
= esk2_0 ),
inference(er,[status(thm)],[inference(choice_inst,[status(thm)],[inference(cn,[status(thm)],[]),c_0_9,c_0_10])]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_11])]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO538^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n009.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:13:45 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running higher-order theorem proving
% 0.10/0.27 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.dHSNWPRD9Q/E---3.1_95949.p
% 0.25/0.29 % Version: 3.5.1-ho
% 0.25/0.29 % Preprocessing class: HSSSSMSSSSSCSFA.
% 0.25/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.29 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.25/0.29 % Starting ho_unfolding_6 with 300s (1) cores
% 0.25/0.29 % Starting sh4l with 300s (1) cores
% 0.25/0.29 % ehoh_best8_lambda with pid 95963 completed with status 0
% 0.25/0.29 % Result found by ehoh_best8_lambda
% 0.25/0.29 % Preprocessing class: HSSSSMSSSSSCSFA.
% 0.25/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.29 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.25/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.25/0.29 % No SInE strategy applied
% 0.25/0.29 % Search class: HHHSF-FFSF11-DSFFFMBC
% 0.25/0.29 % partial match(4): HGHSF-FFSF11-SSSFFMBN
% 0.25/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.29 % SubtermCWHack with pid 95966 completed with status 0
% 0.25/0.29 % Result found by SubtermCWHack
% 0.25/0.29 % Preprocessing class: HSSSSMSSSSSCSFA.
% 0.25/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.29 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.25/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.25/0.29 % No SInE strategy applied
% 0.25/0.29 % Search class: HHHSF-FFSF11-DSFFFMBC
% 0.25/0.29 % partial match(4): HGHSF-FFSF11-SSSFFMBN
% 0.25/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.29 % Preprocessing time : 0.001 s
% 0.25/0.29
% 0.25/0.29 % Proof found!
% 0.25/0.29 % SZS status Theorem
% 0.25/0.29 % SZS output start CNFRefutation
% See solution above
% 0.25/0.29 % Parsed axioms : 5
% 0.25/0.29 % Removed by relevancy pruning/SinE : 0
% 0.25/0.29 % Initial clauses : 4
% 0.25/0.29 % Removed in clause preprocessing : 2
% 0.25/0.29 % Initial clauses in saturation : 2
% 0.25/0.29 % Processed clauses : 5
% 0.25/0.29 % ...of these trivial : 0
% 0.25/0.29 % ...subsumed : 0
% 0.25/0.29 % ...remaining for further processing : 4
% 0.25/0.29 % Other redundant clauses eliminated : 2
% 0.25/0.29 % Clauses deleted for lack of memory : 0
% 0.25/0.29 % Backward-subsumed : 0
% 0.25/0.29 % Backward-rewritten : 1
% 0.25/0.29 % Generated clauses : 6
% 0.25/0.29 % ...of the previous two non-redundant : 5
% 0.25/0.29 % ...aggressively subsumed : 0
% 0.25/0.29 % Contextual simplify-reflections : 0
% 0.25/0.29 % Paramodulations : 0
% 0.25/0.29 % Factorizations : 0
% 0.25/0.29 % NegExts : 0
% 0.25/0.29 % Equation resolutions : 2
% 0.25/0.29 % Disequality decompositions : 0
% 0.25/0.29 % Total rewrite steps : 2
% 0.25/0.29 % ...of those cached : 0
% 0.25/0.29 % Propositional unsat checks : 0
% 0.25/0.29 % Propositional check models : 0
% 0.25/0.29 % Propositional check unsatisfiable : 0
% 0.25/0.29 % Propositional clauses : 0
% 0.25/0.29 % Propositional clauses after purity: 0
% 0.25/0.29 % Propositional unsat core size : 0
% 0.25/0.29 % Propositional preprocessing time : 0.000
% 0.25/0.29 % Propositional encoding time : 0.000
% 0.25/0.29 % Propositional solver time : 0.000
% 0.25/0.29 % Success case prop preproc time : 0.000
% 0.25/0.29 % Success case prop encoding time : 0.000
% 0.25/0.29 % Success case prop solver time : 0.000
% 0.25/0.29 % Current number of processed clauses : 3
% 0.25/0.29 % Positive orientable unit clauses : 2
% 0.25/0.29 % Positive unorientable unit clauses: 0
% 0.25/0.29 % Negative unit clauses : 0
% 0.25/0.29 % Non-unit-clauses : 1
% 0.25/0.29 % Current number of unprocessed clauses: 2
% 0.25/0.29 % ...number of literals in the above : 4
% 0.25/0.29 % Current number of archived formulas : 0
% 0.25/0.29 % Current number of archived clauses : 1
% 0.25/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.29 % Non-unit clause-clause subsumptions : 0
% 0.25/0.29 % Unit Clause-clause subsumption calls : 0
% 0.25/0.29 % Rewrite failures with RHS unbound : 0
% 0.25/0.29 % BW rewrite match attempts : 1
% 0.25/0.29 % BW rewrite match successes : 1
% 0.25/0.29 % Condensation attempts : 0
% 0.25/0.29 % Condensation successes : 0
% 0.25/0.29 % Termbank termtop insertions : 531
% 0.25/0.29 % Search garbage collected termcells : 111
% 0.25/0.29
% 0.25/0.29 % -------------------------------------------------
% 0.25/0.29 % User time : 0.003 s
% 0.25/0.29 % System time : 0.002 s
% 0.25/0.29 % Total time : 0.005 s
% 0.25/0.29 % Maximum resident set size: 3636 pages
% 0.25/0.29
% 0.25/0.29 % -------------------------------------------------
% 0.25/0.29 % User time : 0.004 s
% 0.25/0.29 % System time : 0.007 s
% 0.25/0.29 % Total time : 0.011 s
% 0.25/0.29 % Maximum resident set size: 4864 pages
% 0.25/0.29 % E exiting
%------------------------------------------------------------------------------