%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET669^3 : 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 : n018.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 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 18 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 127 ( 19 ~; 16 |; 10 &; 72 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 61 ( 28 ^; 27 !; 6 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_34,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_39,type,
id_rel: ( $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,
esk1_0: $i ).
thf(decl_60,type,
esk2_0: $i ).
thf(decl_61,type,
esk3_0: $i ).
thf(thm,conjecture,
! [X28: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [X1: $i] : $true )
@ X28 )
=> ( ( subset
@ ^ [X1: $i] : $true
@ ( rel_domain @ X28 ) )
& ( ( ^ [X1: $i] : $true )
= ( rel_codomain @ X28 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zjsv2Q5apx/E---3.1_83553.p',thm) ).
thf(subset,axiom,
( subset
= ( ^ [X16: $i > $o,X17: $i > $o] :
! [X4: $i] :
( ( X16 @ X4 )
=> ( X17 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zjsv2Q5apx/E---3.1_83553.p',subset) ).
thf(id_rel,axiom,
( id_rel
= ( ^ [X25: $i > $o,X1: $i,X3: $i] :
( ( X25 @ X1 )
& ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zjsv2Q5apx/E---3.1_83553.p',id_rel) ).
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.Zjsv2Q5apx/E---3.1_83553.p',sub_rel) ).
thf(rel_codomain,axiom,
( rel_codomain
= ( ^ [X28: $i > $i > $o,X3: $i] :
? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zjsv2Q5apx/E---3.1_83553.p',rel_codomain) ).
thf(rel_domain,axiom,
( rel_domain
= ( ^ [X28: $i > $i > $o,X1: $i] :
? [X3: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Zjsv2Q5apx/E---3.1_83553.p',rel_domain) ).
thf(c_0_6,negated_conjecture,
~ ! [X28: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [X1: $i] : $true )
@ X28 )
=> ( ( subset
@ ^ [X1: $i] : $true
@ ( rel_domain @ X28 ) )
& ( ( ^ [X1: $i] : $true )
= ( rel_codomain @ X28 ) ) ) ),
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,
( id_rel
= ( ^ [Z0: $i > $o,Z1: $i,Z2: $i] :
( ( Z0 @ Z1 )
& ( Z1 = Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[id_rel]) ).
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] :
( ! [X45: $i,X46: $i] :
( ( $true
& ( X45 = X46 ) )
=> ( X28 @ X45 @ X46 ) )
=> ( ! [X48: $i] :
( $true
=> ? [X47: $i] : ( X28 @ X48 @ X47 ) )
& ! [X50: $i] :
( $true
<=> ? [X49: $i] : ( X28 @ X49 @ X50 ) ) ) ),
inference(fof_simplification,[status(thm)],[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)],[inference(fof_simplification,[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,
! [X52: $i,X53: $i,X55: $i,X57: $i] :
( ( ~ $true
| ( X52 != X53 )
| ( epred1_0 @ X52 @ X53 ) )
& ( ~ $true
| ~ ( epred1_0 @ X57 @ esk2_0 )
| $true )
& ( $true
| ( epred1_0 @ esk3_0 @ esk2_0 )
| $true )
& ( ~ $true
| ~ ( epred1_0 @ X57 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X55 ) )
& ( $true
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X55 ) ) ),
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_12])])])])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ X1 @ X3 )
| ~ $true
| ( X1 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ $true
| ~ ( epred1_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred1_0 @ X1 @ X3 )
| ( X1 != X3 ) ),
inference(cn,[status(thm)],[c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred1_0 @ X1 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] : ( epred1_0 @ X1 @ X1 ),
inference(er,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
~ ( epred1_0 @ esk1_0 @ X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_19,c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET669^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.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 13:42:41 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.Zjsv2Q5apx/E---3.1_83553.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 % almost_fo_3_lam with pid 83591 completed with status 0
% 0.08/0.26 % Result found by almost_fo_3_lam
% 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 % (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: HHHSF-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 83593 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 % Starting almost_fo_3_lam 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: HHHSF-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 : 40
% 0.08/0.26 % Removed in clause preprocessing : 38
% 0.08/0.26 % Initial clauses in saturation : 2
% 0.08/0.26 % Processed clauses : 4
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 4
% 0.08/0.26 % Other redundant clauses eliminated : 1
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 1
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 3
% 0.08/0.26 % ...of the previous two non-redundant : 2
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 2
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 1
% 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 : 2
% 0.08/0.26 % Positive orientable unit clauses : 1
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 0
% 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) : 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 : 1
% 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 : 2196
% 0.08/0.26 % Search garbage collected termcells : 318
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.003 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.005 s
% 0.08/0.26 % Maximum resident set size: 3708 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.006 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
%------------------------------------------------------------------------------