%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET651^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:22:17 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 8 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 80 ( 9 ~; 4 |; 5 &; 53 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 41 ( 22 ^; 16 !; 3 ?; 41 :)
% 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_51,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(decl_58,type,
a: $i > $o ).
thf(decl_59,type,
epred1_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] :
( ( subset @ ( rel_domain @ X28 ) @ a )
=> ( sub_rel @ X28
@ ( cartesian_product @ a
@ ^ [X1: $i] : $true ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fYjLUPClnT/E---3.1_1067256.p',thm) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fYjLUPClnT/E---3.1_1067256.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/sandbox2/tmp/tmp.fYjLUPClnT/E---3.1_1067256.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/sandbox2/tmp/tmp.fYjLUPClnT/E---3.1_1067256.p',sub_rel) ).
thf(rel_domain,axiom,
( rel_domain
= ( ^ [X28: $i > $i > $o,X1: $i] :
? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fYjLUPClnT/E---3.1_1067256.p',rel_domain) ).
thf(c_0_5,negated_conjecture,
~ ! [X28: $i > $i > $o] :
( ( subset @ ( rel_domain @ X28 ) @ a )
=> ( sub_rel @ X28
@ ( cartesian_product @ a
@ ^ [X1: $i] : $true ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_6,plain,
( subset
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subset]) ).
thf(c_0_7,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_8,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_9,plain,
( rel_domain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X3: $i] : ( Z0 @ Z1 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[rel_domain]) ).
thf(c_0_10,negated_conjecture,
~ ! [X28: $i > $i > $o] :
( ! [X46: $i] :
( ? [X45: $i] : ( X28 @ X46 @ X45 )
=> ( a @ X46 ) )
=> ! [X47: $i,X48: $i] :
( ( X28 @ X47 @ X48 )
=> ( ( a @ X47 )
& $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5]),c_0_6]),c_0_7]),c_0_8]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X50: $i,X51: $i] :
( ( ~ ( epred1_0 @ X50 @ X51 )
| ( a @ X50 ) )
& ( epred1_0 @ esk1_0 @ esk2_0 )
& ( ~ ( a @ esk1_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_10])])])])]) ).
thf(c_0_12,negated_conjecture,
( ~ ( a @ esk1_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i] :
( ( a @ X1 )
| ~ ( epred1_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ( a @ esk1_0 ),
inference(cn,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET651^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:41:19 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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.fYjLUPClnT/E---3.1_1067256.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.09/0.25 % post_as_ho11 with pid 1067287 completed with status 0
% 0.09/0.25 % Result found by post_as_ho11
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HHUNF-FFSF00-SHSSMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 1067295 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HHUNF-FFSF00-SHSSMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 72
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 39
% 0.09/0.25 % Removed in clause preprocessing : 36
% 0.09/0.25 % Initial clauses in saturation : 3
% 0.09/0.25 % Processed clauses : 3
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 3
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 1
% 0.09/0.25 % ...of the previous two non-redundant : 0
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 1
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 0
% 0.09/0.25 % ...of those cached : 0
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 3
% 0.09/0.25 % Positive orientable unit clauses : 1
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 1
% 0.09/0.25 % Current number of unprocessed clauses: 0
% 0.09/0.25 % ...number of literals in the above : 0
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 0
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 0
% 0.09/0.25 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 1975
% 0.09/0.25 % Search garbage collected termcells : 220
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.002 s
% 0.09/0.25 % System time : 0.004 s
% 0.09/0.25 % Total time : 0.006 s
% 0.09/0.25 % Maximum resident set size: 3708 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.003 s
% 0.09/0.25 % System time : 0.010 s
% 0.09/0.25 % Total time : 0.013 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------