%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO008^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:42:07 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 60 ( 7 ~; 2 |; 2 &; 40 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 28 ( 8 ^; 20 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
leibeq1: $i > $i > $o ).
thf(decl_24,type,
leibeq2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(decl_25,type,
esk1_0: $i > $i ).
thf(decl_26,type,
esk2_0: $i > $i ).
thf(decl_27,type,
epred1_0: ( $i > $i ) > $o ).
thf(conj,conjecture,
! [X7: $i > $i,X8: $i > $i] :
( ! [X9: $i] : ( leibeq1 @ ( X7 @ X9 ) @ ( X8 @ X9 ) )
=> ( leibeq2 @ X7 @ X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.OzqGQKImGe/E---3.1_2694982.p',conj) ).
thf(leibeq1,axiom,
( leibeq1
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OzqGQKImGe/E---3.1_2694982.p',leibeq1) ).
thf(leibeq2,axiom,
( leibeq2
= ( ^ [X4: $i > $i,X5: $i > $i] :
! [X6: ( $i > $i ) > $o] :
( ( X6 @ X4 )
=> ( X6 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OzqGQKImGe/E---3.1_2694982.p',leibeq2) ).
thf(c_0_3,negated_conjecture,
~ ! [X7: $i > $i,X8: $i > $i] :
( ! [X9: $i] : ( leibeq1 @ ( X7 @ X9 ) @ ( X8 @ X9 ) )
=> ( leibeq2 @ X7 @ X8 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_4,plain,
( leibeq1
= ( ^ [Z0: $i,Z1: $i] :
! [X3: $i > $o] :
( ( X3 @ Z0 )
=> ( X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[leibeq1]) ).
thf(c_0_5,plain,
( leibeq2
= ( ^ [Z0: $i > $i,Z1: $i > $i] :
! [X6: ( $i > $i ) > $o] :
( ( X6 @ Z0 )
=> ( X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[leibeq2]) ).
thf(c_0_6,negated_conjecture,
~ ! [X7: $i > $i,X8: $i > $i] :
( ! [X9: $i,X13: $i > $o] :
( ( X13 @ ( X7 @ X9 ) )
=> ( X13 @ ( X8 @ X9 ) ) )
=> ! [X14: ( $i > $i ) > $o] :
( ( X14 @ X7 )
=> ( X14 @ X8 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,c_0_4]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X17: $i,X18: $i > $o] :
( ( ~ ( X18 @ ( esk1_0 @ X17 ) )
| ( X18 @ ( esk2_0 @ X17 ) ) )
& ( epred1_0 @ esk1_0 )
& ~ ( epred1_0 @ esk2_0 ) ),
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_6])])])])]) ).
thf(c_0_8,negated_conjecture,
~ ( epred1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
epred1_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i > $o,X1: $i] :
( ( X3 @ ( esk2_0 @ X1 ) )
| ~ ( X3 @ ( esk1_0 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
esk1_0 != esk2_0,
inference(ext_sup,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( esk1_0 @ X1 )
= ( esk2_0 @ X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_10]) ).
thf(c_0_13,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO008^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.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 16:22:58 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 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.OzqGQKImGe/E---3.1_2694982.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNHSN.
% 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 lpo8_lambda_fix with 300s (1) cores
% 0.08/0.26 % Starting lpo8_s with 300s (1) cores
% 0.08/0.26 % Starting new_bool_11 with 300s (1) cores
% 0.08/0.26 % ho_unfolding_3 with pid 2694995 completed with status 0
% 0.08/0.26 % Result found by ho_unfolding_3
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNHSN.
% 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 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHUNF-FFSF00-SHSFMSBN
% 0.08/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.26 % Starting ho_unfolding_3 with 901s (1) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.08/0.26 % Starting sh5l with 151s (1) cores
% 0.08/0.26 % Starting new_bool_3 with 146s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 2694999 completed with status 10
% 0.08/0.26 % ehoh_best_sine_rwall with pid 2695001 completed with status 0
% 0.08/0.26 % Result found by ehoh_best_sine_rwall
% 0.08/0.26 % Preprocessing class: HSSSSMSSSLSNHSN.
% 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 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHUNF-FFSF00-SHSFMSBN
% 0.08/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.26 % Starting ho_unfolding_3 with 901s (1) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 151s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26 % Presaturation interreduction done
% 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 : 5
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 5
% 0.08/0.26 % Removed in clause preprocessing : 2
% 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 : 0
% 0.08/0.26 % Backward-rewritten : 1
% 0.08/0.26 % Generated clauses : 7
% 0.08/0.26 % ...of the previous two non-redundant : 4
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 0
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 1
% 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 : 0
% 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 : 4
% 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 : 0
% 0.08/0.26 % Current number of unprocessed clauses: 2
% 0.08/0.26 % ...number of literals in the above : 2
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 4
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 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 : 2
% 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 : 459
% 0.08/0.26 % Search garbage collected termcells : 142
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.002 s
% 0.08/0.26 % System time : 0.004 s
% 0.08/0.26 % Total time : 0.006 s
% 0.08/0.26 % Maximum resident set size: 3840 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.009 s
% 0.08/0.26 % System time : 0.009 s
% 0.08/0.26 % Total time : 0.018 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------