%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU970^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:26:01 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 166 ( 20 ~; 19 |; 14 &; 100 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 4 ^; 27 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
s: $i > $i ).
thf(decl_24,type,
cCKB_E2: $i > $i > $o ).
thf(decl_25,type,
esk1_0: $i ).
thf(decl_26,type,
esk2_0: $i ).
thf(decl_27,type,
esk3_0: $i ).
thf(decl_28,type,
esk4_1: ( $i > $o ) > $i ).
thf(decl_29,type,
esk5_1: ( $i > $o ) > $i ).
thf(decl_30,type,
epred1_0: $i > $o ).
thf(cCKB_L34000_pme,conjecture,
! [X1: $i,X2: $i,X5: $i] :
( ( ( cCKB_E2 @ X1 @ X2 )
& ( cCKB_E2 @ X2 @ X5 ) )
=> ( cCKB_E2 @ X1 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.yPxAcYRCCN/E---3.1_453160.p',cCKB_L34000_pme) ).
thf(cCKB_E2_def,axiom,
( cCKB_E2
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( s @ ( s @ X4 ) ) ) ) )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yPxAcYRCCN/E---3.1_453160.p',cCKB_E2_def) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: $i,X2: $i,X5: $i] :
( ( ( cCKB_E2 @ X1 @ X2 )
& ( cCKB_E2 @ X2 @ X5 ) )
=> ( cCKB_E2 @ X1 @ X5 ) ),
inference(assume_negation,[status(cth)],[cCKB_L34000_pme]) ).
thf(c_0_3,plain,
( cCKB_E2
= ( ^ [Z0: $i,Z1: $i] :
! [X3: $i > $o] :
( ( ( X3 @ Z0 )
& ! [X4: $i] :
( ( X3 @ X4 )
=> ( X3 @ ( s @ ( s @ X4 ) ) ) ) )
=> ( X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB_E2_def]) ).
thf(c_0_4,negated_conjecture,
~ ! [X1: $i,X2: $i,X5: $i] :
( ( ! [X9: $i > $o] :
( ( ( X9 @ X1 )
& ! [X10: $i] :
( ( X9 @ X10 )
=> ( X9 @ ( s @ ( s @ X10 ) ) ) ) )
=> ( X9 @ X2 ) )
& ! [X11: $i > $o] :
( ( ( X11 @ X2 )
& ! [X12: $i] :
( ( X11 @ X12 )
=> ( X11 @ ( s @ ( s @ X12 ) ) ) ) )
=> ( X11 @ X5 ) ) )
=> ! [X13: $i > $o] :
( ( ( X13 @ X1 )
& ! [X14: $i] :
( ( X13 @ X14 )
=> ( X13 @ ( s @ ( s @ X14 ) ) ) ) )
=> ( X13 @ X5 ) ) ),
inference(apply_def,[status(thm)],[c_0_2,c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X18: $i > $o,X20: $i > $o,X23: $i] :
( ( ( X18 @ ( esk4_1 @ X18 ) )
| ~ ( X18 @ esk1_0 )
| ( X18 @ esk2_0 ) )
& ( ~ ( X18 @ ( s @ ( s @ ( esk4_1 @ X18 ) ) ) )
| ~ ( X18 @ esk1_0 )
| ( X18 @ esk2_0 ) )
& ( ( X20 @ ( esk5_1 @ X20 ) )
| ~ ( X20 @ esk2_0 )
| ( X20 @ esk3_0 ) )
& ( ~ ( X20 @ ( s @ ( s @ ( esk5_1 @ X20 ) ) ) )
| ~ ( X20 @ esk2_0 )
| ( X20 @ esk3_0 ) )
& ( epred1_0 @ esk1_0 )
& ( ~ ( epred1_0 @ X23 )
| ( epred1_0 @ ( s @ ( s @ X23 ) ) ) )
& ~ ( epred1_0 @ esk3_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ esk2_0 )
| ~ ( X3 @ ( s @ ( s @ ( esk4_1 @ X3 ) ) ) )
| ~ ( X3 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ ( s @ ( s @ X1 ) ) )
| ~ ( epred1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
epred1_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ ( esk4_1 @ epred1_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ ( esk4_1 @ X3 ) )
| ( X3 @ esk2_0 )
| ~ ( X3 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ esk3_0 )
| ~ ( X3 @ ( s @ ( s @ ( esk5_1 @ X3 ) ) ) )
| ~ ( X3 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
epred1_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8])]) ).
thf(c_0_13,negated_conjecture,
~ ( epred1_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_14,negated_conjecture,
~ ( epred1_0 @ ( esk5_1 @ epred1_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_7]),c_0_12])]),c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i > $o] :
( ( X3 @ ( esk5_1 @ X3 ) )
| ( X3 @ esk3_0 )
| ~ ( X3 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU970^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:59:32 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.yPxAcYRCCN/E---3.1_453160.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 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 post_as_ho5 with 300s (1) cores
% 0.08/0.26 % Starting sh4l with 300s (1) cores
% 0.08/0.26 % Starting ho_unfolding_2 with 300s (1) cores
% 0.08/0.26 % post_as_ho5 with pid 453174 completed with status 0
% 0.08/0.26 % Result found by post_as_ho5
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 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 post_as_ho5 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.08/0.26 % Search class: HGUNF-FFSF11-MSFFMMBN
% 0.08/0.26 % partial match(1): HGUNF-FFSF11-MSFFMSBN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 453178 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNSFN.
% 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 post_as_ho5 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.08/0.26 % Search class: HGUNF-FFSF11-MSFFMMBN
% 0.08/0.26 % partial match(1): HGUNF-FFSF11-MSFFMSBN
% 0.08/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 31s (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 : 4
% 0.08/0.26 % Removed by relevancy pruning/SinE : 2
% 0.08/0.26 % Initial clauses : 7
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 7
% 0.08/0.26 % Processed clauses : 10
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 10
% 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 : 0
% 0.08/0.26 % Backward-rewritten : 1
% 0.08/0.26 % Generated clauses : 4
% 0.08/0.26 % ...of the previous two non-redundant : 3
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 4
% 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 : 5
% 0.08/0.26 % ...of those cached : 3
% 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 : 9
% 0.08/0.26 % Positive orientable unit clauses : 2
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 2
% 0.08/0.26 % Non-unit-clauses : 5
% 0.08/0.26 % Current number of unprocessed clauses: 0
% 0.08/0.26 % ...number of literals in the above : 0
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 1
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 2
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 2
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 1
% 0.08/0.26 % BW rewrite match successes : 1
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1004
% 0.08/0.26 % Search garbage collected termcells : 355
% 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 : 0.006 s
% 0.08/0.26 % Maximum resident set size: 3580 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.007 s
% 0.08/0.26 % Total time : 0.012 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------