%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET640^3 : TPTP v9.3.1. Released v3.6.0.
% 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 08:22:16 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 53 ( 5 ~; 1 |; 4 &; 36 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 32 ( 16 ^; 16 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_37,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(decl_40,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_58,type,
epred1_0: $i > $i > $o ).
thf(decl_59,type,
epred2_0: $i > $i > $o ).
thf(decl_60,type,
esk1_0: $i ).
thf(decl_61,type,
esk2_0: $i ).
thf(thm,conjecture,
! [X28: $i > $i > $o,X36: $i > $i > $o] :
( ( sub_rel @ X28 @ X36 )
=> ( sub_rel @ X28
@ ( cartesian_product
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fd6X8HMRKG/E---3.1_3541834.p',thm) ).
thf(cartesian_product,axiom,
( cartesian_product
= ( ^ [X22: $i > $o,X23: $i > $o,X4: $i,X24: $i] :
( ( X22 @ X4 )
& ( X23 @ X24 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fd6X8HMRKG/E---3.1_3541834.p',cartesian_product) ).
thf(sub_rel,axiom,
( sub_rel
= ( ^ [X26: $i > $i > $o,X27: $i > $i > $o] :
! [X1: $i,X3: $i] :
( ( X26 @ X1 @ X3 )
=> ( X27 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fd6X8HMRKG/E---3.1_3541834.p',sub_rel) ).
thf(c_0_3,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $i > $o] :
( ( sub_rel @ X28 @ X36 )
=> ( sub_rel @ X28
@ ( cartesian_product
@ ^ [X1: $i] : $true
@ ^ [X1: $i] : $true ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,plain,
( cartesian_product
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i,Z3: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z3 ) ) ) ),
inference(fof_simplification,[status(thm)],[cartesian_product]) ).
thf(c_0_5,plain,
( sub_rel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X1: $i,X3: $i] :
( ( Z0 @ X1 @ X3 )
=> ( Z1 @ X1 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[sub_rel]) ).
thf(c_0_6,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $i > $o] :
( ! [X47: $i,X48: $i] :
( ( X28 @ X47 @ X48 )
=> ( X36 @ X47 @ X48 ) )
=> ! [X49: $i,X50: $i] :
( ( X28 @ X49 @ X50 )
=> $true ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4]),c_0_5])]) ).
thf(c_0_7,negated_conjecture,
! [X53: $i,X54: $i] :
( ( ~ ( epred1_0 @ X53 @ X54 )
| ( epred2_0 @ X53 @ X54 ) )
& ( epred1_0 @ esk1_0 @ esk2_0 )
& ~ $true ),
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,
~ $true,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
$false,
inference(cn,[status(thm)],[c_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET640^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n015.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 13:43:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.fd6X8HMRKG/E---3.1_3541834.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 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_best2_full_lfho with 300s (1) cores
% 0.08/0.26 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.26 % ehoh_best2_full_lfho with pid 3541866 completed with status 0
% 0.08/0.26 % Result found by ehoh_best2_full_lfho
% 0.08/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 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_best2_full_lfho with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHHNF-FFSF00-SHSSMFNN
% 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 3541872 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSMSSMSSMLMNHSN.
% 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_best2_full_lfho with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHHNF-FFSF00-SHSSMFNN
% 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 : 71
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 38
% 0.08/0.26 % Removed in clause preprocessing : 35
% 0.08/0.26 % Initial clauses in saturation : 3
% 0.08/0.26 % Processed clauses : 1
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 0
% 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 : 0
% 0.08/0.26 % Generated clauses : 0
% 0.08/0.26 % ...of the previous two non-redundant : 0
% 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 : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 0
% 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 : 0
% 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 : 0
% 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 : 3
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 0
% 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 : 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 : 1914
% 0.08/0.26 % Search garbage collected termcells : 207
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.005 s
% 0.08/0.26 % System time : 0.001 s
% 0.08/0.26 % Total time : 0.006 s
% 0.08/0.26 % Maximum resident set size: 3656 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.008 s
% 0.08/0.26 % System time : 0.006 s
% 0.08/0.26 % Total time : 0.014 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------