%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET649^3 : 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 : n007.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 0.28s 0.27s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 10 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 11 ~; 6 |; 9 &; 76 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 57 ( 24 ^; 27 !; 6 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_34,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
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_50,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(decl_51,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(decl_58,type,
epred1_0: $i > $i > $o ).
thf(decl_59,type,
epred2_0: $i > $o ).
thf(decl_60,type,
epred3_0: $i > $o ).
thf(decl_61,type,
esk1_0: $i ).
thf(decl_62,type,
esk2_0: $i ).
thf(thm,conjecture,
! [X28: $i > $i > $o,X36: $i > $o,X37: $i > $o] :
( ( ( subset @ ( rel_domain @ X28 ) @ X36 )
& ( subset @ ( rel_codomain @ X28 ) @ X37 ) )
=> ( sub_rel @ X28 @ ( cartesian_product @ X36 @ X37 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cooQvecBws/E---3.1_3371348.p',thm) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cooQvecBws/E---3.1_3371348.p',subset) ).
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.cooQvecBws/E---3.1_3371348.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.cooQvecBws/E---3.1_3371348.p',sub_rel) ).
thf(rel_codomain,axiom,
( rel_codomain
= ( ^ [X28: $i > $i > $o,X3: $i] :
? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cooQvecBws/E---3.1_3371348.p',rel_codomain) ).
thf(rel_domain,axiom,
( rel_domain
= ( ^ [X28: $i > $i > $o,X1: $i] :
? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cooQvecBws/E---3.1_3371348.p',rel_domain) ).
thf(c_0_6,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $o,X37: $i > $o] :
( ( ( subset @ ( rel_domain @ X28 ) @ X36 )
& ( subset @ ( rel_codomain @ X28 ) @ X37 ) )
=> ( sub_rel @ X28 @ ( cartesian_product @ X36 @ X37 ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,plain,
( subset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_8,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_9,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_10,plain,
( rel_codomain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X1: $i] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[rel_codomain]) ).
thf(c_0_11,plain,
( rel_domain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X3: $i] : ( Z0 @ Z1 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[rel_domain]) ).
thf(c_0_12,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $o,X37: $i > $o] :
( ( ! [X50: $i] :
( ? [X49: $i] : ( X28 @ X50 @ X49 )
=> ( X36 @ X50 ) )
& ! [X52: $i] :
( ? [X51: $i] : ( X28 @ X51 @ X52 )
=> ( X37 @ X52 ) ) )
=> ! [X53: $i,X54: $i] :
( ( X28 @ X53 @ X54 )
=> ( ( X36 @ X53 )
& ( X37 @ X54 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X58: $i,X59: $i,X60: $i,X61: $i] :
( ( ~ ( epred1_0 @ X58 @ X59 )
| ( epred2_0 @ X58 ) )
& ( ~ ( epred1_0 @ X61 @ X60 )
| ( epred3_0 @ X60 ) )
& ( epred1_0 @ esk1_0 @ esk2_0 )
& ( ~ ( epred2_0 @ esk1_0 )
| ~ ( epred3_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_12])])])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ~ ( epred2_0 @ esk1_0 )
| ~ ( epred3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
epred2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred3_0 @ X3 )
| ~ ( epred1_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
~ ( epred3_0 @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET649^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:38:25 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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.cooQvecBws/E---3.1_3371348.p
% 0.28/0.27 % Version: 3.5.1-ho
% 0.28/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.28/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.27 % Starting post_as_ho11 with 300s (1) cores
% 0.28/0.27 % Starting full_lambda_8 with 300s (1) cores
% 0.28/0.27 % post_as_ho3 with pid 3371384 completed with status 0
% 0.28/0.27 % Result found by post_as_ho3
% 0.28/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.28/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.27 % No SInE strategy applied
% 0.28/0.27 % Search class: HHHNF-FFSF00-SHSSMFNN
% 0.28/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.27 % SubtermCWHack with pid 3371387 completed with status 0
% 0.28/0.27 % Result found by SubtermCWHack
% 0.28/0.27 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.28/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.27 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.27 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.27 % No SInE strategy applied
% 0.28/0.27 % Search class: HHHNF-FFSF00-SHSSMFNN
% 0.28/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.27 % Preprocessing time : 0.001 s
% 0.28/0.27
% 0.28/0.27 % Proof found!
% 0.28/0.27 % SZS status Theorem
% 0.28/0.27 % SZS output start CNFRefutation
% See solution above
% 0.28/0.27 % Parsed axioms : 71
% 0.28/0.27 % Removed by relevancy pruning/SinE : 0
% 0.28/0.27 % Initial clauses : 39
% 0.28/0.27 % Removed in clause preprocessing : 35
% 0.28/0.27 % Initial clauses in saturation : 4
% 0.28/0.27 % Processed clauses : 6
% 0.28/0.27 % ...of these trivial : 0
% 0.28/0.27 % ...subsumed : 0
% 0.28/0.27 % ...remaining for further processing : 6
% 0.28/0.27 % Other redundant clauses eliminated : 0
% 0.28/0.27 % Clauses deleted for lack of memory : 0
% 0.28/0.27 % Backward-subsumed : 0
% 0.28/0.27 % Backward-rewritten : 1
% 0.28/0.27 % Generated clauses : 2
% 0.28/0.27 % ...of the previous two non-redundant : 2
% 0.28/0.27 % ...aggressively subsumed : 0
% 0.28/0.27 % Contextual simplify-reflections : 0
% 0.28/0.27 % Paramodulations : 2
% 0.28/0.27 % Factorizations : 0
% 0.28/0.27 % NegExts : 0
% 0.28/0.27 % Equation resolutions : 0
% 0.28/0.27 % Disequality decompositions : 0
% 0.28/0.27 % Total rewrite steps : 1
% 0.28/0.27 % ...of those cached : 0
% 0.28/0.27 % Propositional unsat checks : 0
% 0.28/0.27 % Propositional check models : 0
% 0.28/0.27 % Propositional check unsatisfiable : 0
% 0.28/0.27 % Propositional clauses : 0
% 0.28/0.27 % Propositional clauses after purity: 0
% 0.28/0.27 % Propositional unsat core size : 0
% 0.28/0.27 % Propositional preprocessing time : 0.000
% 0.28/0.27 % Propositional encoding time : 0.000
% 0.28/0.27 % Propositional solver time : 0.000
% 0.28/0.27 % Success case prop preproc time : 0.000
% 0.28/0.27 % Success case prop encoding time : 0.000
% 0.28/0.27 % Success case prop solver time : 0.000
% 0.28/0.27 % Current number of processed clauses : 5
% 0.28/0.27 % Positive orientable unit clauses : 2
% 0.28/0.27 % Positive unorientable unit clauses: 0
% 0.28/0.27 % Negative unit clauses : 1
% 0.28/0.27 % Non-unit-clauses : 2
% 0.28/0.27 % Current number of unprocessed clauses: 0
% 0.28/0.27 % ...number of literals in the above : 0
% 0.28/0.27 % Current number of archived formulas : 0
% 0.28/0.27 % Current number of archived clauses : 1
% 0.28/0.27 % Clause-clause subsumption calls (NU) : 0
% 0.28/0.27 % Rec. Clause-clause subsumption calls : 0
% 0.28/0.27 % Non-unit clause-clause subsumptions : 0
% 0.28/0.27 % Unit Clause-clause subsumption calls : 0
% 0.28/0.27 % Rewrite failures with RHS unbound : 0
% 0.28/0.27 % BW rewrite match attempts : 1
% 0.28/0.27 % BW rewrite match successes : 1
% 0.28/0.27 % Condensation attempts : 0
% 0.28/0.27 % Condensation successes : 0
% 0.28/0.27 % Termbank termtop insertions : 2151
% 0.28/0.27 % Search garbage collected termcells : 333
% 0.28/0.27
% 0.28/0.27 % -------------------------------------------------
% 0.28/0.27 % User time : 0.004 s
% 0.28/0.27 % System time : 0.002 s
% 0.28/0.27 % Total time : 0.005 s
% 0.28/0.27 % Maximum resident set size: 3708 pages
% 0.28/0.27
% 0.28/0.27 % -------------------------------------------------
% 0.28/0.27 % User time : 0.008 s
% 0.28/0.27 % System time : 0.004 s
% 0.28/0.27 % Total time : 0.013 s
% 0.28/0.27 % Maximum resident set size: 4864 pages
% 0.28/0.27 % E exiting
%------------------------------------------------------------------------------