%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET683^3 : 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 : n011.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 08:22:48 AM UTC 2026
% Result : Theorem 0.10s 0.27s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 10 ~; 5 |; 10 &; 66 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 14 ^; 28 !; 9 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_41,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $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] :
( ( is_rel_on @ X28 @ X36 @ X37 )
=> ! [X24: $i] :
( ( X37 @ X24 )
=> ( ( rel_codomain @ X28 @ X24 )
=> ? [X4: $i] :
( ( X36 @ X4 )
& ( rel_domain @ X28 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lkYkJ8cQEw/E---3.1_108959.p',thm) ).
thf(is_rel_on,axiom,
( is_rel_on
= ( ^ [X28: $i > $i > $o,X29: $i > $o,X30: $i > $o] :
! [X1: $i,X3: $i] :
( ( X28 @ X1 @ X3 )
=> ( ( X29 @ X1 )
& ( X30 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lkYkJ8cQEw/E---3.1_108959.p',is_rel_on) ).
thf(rel_codomain,axiom,
( rel_codomain
= ( ^ [X28: $i > $i > $o,X3: $i] :
? [X1: $i] : ( X28 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lkYkJ8cQEw/E---3.1_108959.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.lkYkJ8cQEw/E---3.1_108959.p',rel_domain) ).
thf(c_0_4,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $o,X37: $i > $o] :
( ( is_rel_on @ X28 @ X36 @ X37 )
=> ! [X24: $i] :
( ( X37 @ X24 )
=> ( ( rel_codomain @ X28 @ X24 )
=> ? [X4: $i] :
( ( X36 @ X4 )
& ( rel_domain @ X28 @ X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_5,plain,
( is_rel_on
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i > $o] :
! [X1: $i,X3: $i] :
( ( Z0 @ X1 @ X3 )
=> ( ( Z1 @ X1 )
& ( Z2 @ X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[is_rel_on]) ).
thf(c_0_6,plain,
( rel_codomain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X1: $i] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[rel_codomain]) ).
thf(c_0_7,plain,
( rel_domain
= ( ^ [Z0: $i > $i > $o,Z1: $i] :
? [X3: $i] : ( Z0 @ Z1 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[rel_domain]) ).
thf(c_0_8,negated_conjecture,
~ ! [X28: $i > $i > $o,X36: $i > $o,X37: $i > $o] :
( ! [X43: $i,X44: $i] :
( ( X28 @ X43 @ X44 )
=> ( ( X36 @ X43 )
& ( X37 @ X44 ) ) )
=> ! [X24: $i] :
( ( X37 @ X24 )
=> ( ? [X45: $i] : ( X28 @ X45 @ X24 )
=> ? [X4: $i] :
( ( X36 @ X4 )
& ? [X46: $i] : ( X28 @ X4 @ X46 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]),c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X50: $i,X51: $i,X54: $i,X55: $i] :
( ( ( epred2_0 @ X50 )
| ~ ( epred1_0 @ X50 @ X51 ) )
& ( ( epred3_0 @ X51 )
| ~ ( epred1_0 @ X50 @ X51 ) )
& ( epred3_0 @ esk1_0 )
& ( epred1_0 @ esk2_0 @ esk1_0 )
& ( ~ ( epred2_0 @ X54 )
| ~ ( epred1_0 @ X54 @ 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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred2_0 @ X1 )
| ~ ( epred1_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
epred1_0 @ esk2_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i] :
~ ( epred1_0 @ X1 @ X3 ),
inference(csr,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_12,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET683^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n011.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:40:46 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 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.lkYkJ8cQEw/E---3.1_108959.p
% 0.10/0.27 % Version: 3.5.1-ho
% 0.10/0.27 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting sh5l with 300s (1) cores
% 0.10/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.27 % Starting new_bool_2 with 300s (1) cores
% 0.10/0.27 % new_bool_1 with pid 108974 completed with status 0
% 0.10/0.27 % Result found by new_bool_1
% 0.10/0.27 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting sh5l with 300s (1) cores
% 0.10/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.27 % Search class: HHHNF-FFSF00-SHSSMFNN
% 0.10/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.27 % SubtermCWHack with pid 108976 completed with status 0
% 0.10/0.27 % Result found by SubtermCWHack
% 0.10/0.27 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.10/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.27 % Starting sh5l with 300s (1) cores
% 0.10/0.27 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.27 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.27 % Search class: HHHNF-FFSF00-SHSSMFNN
% 0.10/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.27 % Preprocessing time : 0.001 s
% 0.10/0.27
% 0.10/0.27 % Proof found!
% 0.10/0.27 % SZS status Theorem
% 0.10/0.27 % SZS output start CNFRefutation
% See solution above
% 0.10/0.27 % Parsed axioms : 71
% 0.10/0.27 % Removed by relevancy pruning/SinE : 67
% 0.10/0.27 % Initial clauses : 5
% 0.10/0.27 % Removed in clause preprocessing : 0
% 0.10/0.27 % Initial clauses in saturation : 5
% 0.10/0.27 % Processed clauses : 6
% 0.10/0.27 % ...of these trivial : 0
% 0.10/0.27 % ...subsumed : 0
% 0.10/0.27 % ...remaining for further processing : 6
% 0.10/0.27 % Other redundant clauses eliminated : 0
% 0.10/0.27 % Clauses deleted for lack of memory : 0
% 0.10/0.27 % Backward-subsumed : 2
% 0.10/0.27 % Backward-rewritten : 0
% 0.10/0.27 % Generated clauses : 3
% 0.10/0.27 % ...of the previous two non-redundant : 1
% 0.10/0.27 % ...aggressively subsumed : 0
% 0.10/0.27 % Contextual simplify-reflections : 1
% 0.10/0.27 % Paramodulations : 2
% 0.10/0.27 % Factorizations : 0
% 0.10/0.27 % NegExts : 0
% 0.10/0.27 % Equation resolutions : 0
% 0.10/0.27 % Disequality decompositions : 0
% 0.10/0.27 % Total rewrite steps : 1
% 0.10/0.27 % ...of those cached : 0
% 0.10/0.27 % Propositional unsat checks : 0
% 0.10/0.27 % Propositional check models : 0
% 0.10/0.27 % Propositional check unsatisfiable : 0
% 0.10/0.27 % Propositional clauses : 0
% 0.10/0.27 % Propositional clauses after purity: 0
% 0.10/0.27 % Propositional unsat core size : 0
% 0.10/0.27 % Propositional preprocessing time : 0.000
% 0.10/0.27 % Propositional encoding time : 0.000
% 0.10/0.27 % Propositional solver time : 0.000
% 0.10/0.27 % Success case prop preproc time : 0.000
% 0.10/0.27 % Success case prop encoding time : 0.000
% 0.10/0.27 % Success case prop solver time : 0.000
% 0.10/0.27 % Current number of processed clauses : 3
% 0.10/0.27 % Positive orientable unit clauses : 2
% 0.10/0.27 % Positive unorientable unit clauses: 0
% 0.10/0.27 % Negative unit clauses : 1
% 0.10/0.27 % Non-unit-clauses : 0
% 0.10/0.27 % Current number of unprocessed clauses: 0
% 0.10/0.27 % ...number of literals in the above : 0
% 0.10/0.27 % Current number of archived formulas : 0
% 0.10/0.27 % Current number of archived clauses : 3
% 0.10/0.27 % Clause-clause subsumption calls (NU) : 1
% 0.10/0.27 % Rec. Clause-clause subsumption calls : 1
% 0.10/0.27 % Non-unit clause-clause subsumptions : 1
% 0.10/0.27 % Unit Clause-clause subsumption calls : 2
% 0.10/0.27 % Rewrite failures with RHS unbound : 0
% 0.10/0.27 % BW rewrite match attempts : 0
% 0.10/0.27 % BW rewrite match successes : 0
% 0.10/0.27 % Condensation attempts : 0
% 0.10/0.27 % Condensation successes : 0
% 0.10/0.27 % Termbank termtop insertions : 950
% 0.10/0.27 % Search garbage collected termcells : 524
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.003 s
% 0.10/0.27 % System time : 0.001 s
% 0.10/0.27 % Total time : 0.004 s
% 0.10/0.27 % Maximum resident set size: 3968 pages
% 0.10/0.27
% 0.10/0.27 % -------------------------------------------------
% 0.10/0.27 % User time : 0.006 s
% 0.10/0.27 % System time : 0.006 s
% 0.10/0.27 % Total time : 0.012 s
% 0.10/0.27 % Maximum resident set size: 4864 pages
% 0.10/0.27 % E exiting
%------------------------------------------------------------------------------