%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU462^1 : 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 : n009.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 08:26:05 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 369 ( 23 ~; 34 |; 24 &; 269 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 15 ^; 65 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_35,type,
trans: ( $i > $i > $o ) > $o ).
thf(decl_36,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_52,type,
epred1_0: $i > $i > $o ).
thf(decl_53,type,
esk1_0: $i ).
thf(decl_54,type,
esk2_0: $i ).
thf(decl_55,type,
epred2_0: $i > $i > $o ).
thf(decl_56,type,
esk3_1: ( $i > $i > $o ) > $i ).
thf(decl_57,type,
esk4_1: ( $i > $i > $o ) > $i ).
thf(decl_58,type,
esk5_1: ( $i > $i > $o ) > $i ).
thf(decl_59,type,
esk6_1: ( $i > $i > $o ) > $i ).
thf(decl_60,type,
esk7_1: ( $i > $i > $o ) > $i ).
thf(transitive_closure,axiom,
( tc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HpAnPgYVjk/E---3.1_4008544.p',transitive_closure) ).
thf(transitive,axiom,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X6 ) )
=> ( X1 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HpAnPgYVjk/E---3.1_4008544.p',transitive) ).
thf(subrel,axiom,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HpAnPgYVjk/E---3.1_4008544.p',subrel) ).
thf(transitive_closure_is_transitive2,conjecture,
! [X1: $i > $i > $o,X3: $i,X4: $i,X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 )
& ( tc @ X1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) ),
file('/export/starexec/sandbox/tmp/tmp.HpAnPgYVjk/E---3.1_4008544.p',transitive_closure_is_transitive2) ).
thf(c_0_4,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X19: $i,X20: $i,X21: $i] :
( ( ( X2 @ X19 @ X20 )
& ( X2 @ X20 @ X21 ) )
=> ( X2 @ X19 @ X21 ) )
& ! [X22: $i,X23: $i] :
( ( Z0 @ X22 @ X23 )
=> ( X2 @ X22 @ X23 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_closure]) ).
thf(c_0_5,plain,
( trans
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X6 ) )
=> ( Z0 @ X3 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_6,plain,
( subrel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ( Z1 @ X3 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subrel]) ).
thf(c_0_7,negated_conjecture,
~ ! [X1: $i > $i > $o,X3: $i,X4: $i,X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 )
& ( tc @ X1 @ X3 @ X4 ) )
=> ( X2 @ X3 @ X4 ) ),
inference(assume_negation,[status(cth)],[transitive_closure_is_transitive2]) ).
thf(c_0_8,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X19: $i,X20: $i,X21: $i] :
( ( ( X2 @ X19 @ X20 )
& ( X2 @ X20 @ X21 ) )
=> ( X2 @ X19 @ X21 ) )
& ! [X22: $i,X23: $i] :
( ( Z0 @ X22 @ X23 )
=> ( X2 @ X22 @ X23 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
thf(c_0_9,negated_conjecture,
~ ! [X1: $i > $i > $o,X3: $i,X4: $i,X2: $i > $i > $o] :
( ( ! [X161: $i,X162: $i,X163: $i] :
( ( ( X2 @ X161 @ X162 )
& ( X2 @ X162 @ X163 ) )
=> ( X2 @ X161 @ X163 ) )
& ! [X164: $i,X165: $i] :
( ( X1 @ X164 @ X165 )
=> ( X2 @ X164 @ X165 ) )
& ! [X166: $i > $i > $o] :
( ( ! [X167: $i,X168: $i,X169: $i] :
( ( ( X166 @ X167 @ X168 )
& ( X166 @ X168 @ X169 ) )
=> ( X166 @ X167 @ X169 ) )
& ! [X170: $i,X171: $i] :
( ( X1 @ X170 @ X171 )
=> ( X166 @ X170 @ X171 ) ) )
=> ( X166 @ X3 @ X4 ) ) )
=> ( X2 @ X3 @ X4 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_5]),c_0_6]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X176: $i,X177: $i,X178: $i,X179: $i,X180: $i,X181: $i > $i > $o] :
( ( ~ ( epred2_0 @ X176 @ X177 )
| ~ ( epred2_0 @ X177 @ X178 )
| ( epred2_0 @ X176 @ X178 ) )
& ( ~ ( epred1_0 @ X179 @ X180 )
| ( epred2_0 @ X179 @ X180 ) )
& ( ( epred1_0 @ ( esk6_1 @ X181 ) @ ( esk7_1 @ X181 ) )
| ( X181 @ ( esk3_1 @ X181 ) @ ( esk4_1 @ X181 ) )
| ( X181 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X181 @ ( esk6_1 @ X181 ) @ ( esk7_1 @ X181 ) )
| ( X181 @ ( esk3_1 @ X181 ) @ ( esk4_1 @ X181 ) )
| ( X181 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ ( esk6_1 @ X181 ) @ ( esk7_1 @ X181 ) )
| ( X181 @ ( esk4_1 @ X181 ) @ ( esk5_1 @ X181 ) )
| ( X181 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X181 @ ( esk6_1 @ X181 ) @ ( esk7_1 @ X181 ) )
| ( X181 @ ( esk4_1 @ X181 ) @ ( esk5_1 @ X181 ) )
| ( X181 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ ( esk6_1 @ X181 ) @ ( esk7_1 @ X181 ) )
| ~ ( X181 @ ( esk3_1 @ X181 ) @ ( esk5_1 @ X181 ) )
| ( X181 @ esk1_0 @ esk2_0 ) )
& ( ~ ( X181 @ ( esk6_1 @ X181 ) @ ( esk7_1 @ X181 ) )
| ~ ( X181 @ ( esk3_1 @ X181 ) @ ( esk5_1 @ X181 ) )
| ( X181 @ esk1_0 @ esk2_0 ) )
& ~ ( epred2_0 @ esk1_0 @ esk2_0 ) ),
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_9])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i,X4: $i,X6: $i] :
( ( epred2_0 @ X3 @ X6 )
| ~ ( epred2_0 @ X3 @ X4 )
| ~ ( epred2_0 @ X4 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( epred2_0 @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ) )
| ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 @ ( esk4_1 @ epred2_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( X1 @ ( esk3_1 @ X1 ) @ ( esk4_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk3_1 @ X1 ) @ ( esk5_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,negated_conjecture,
( ( epred2_0 @ ( esk3_1 @ epred2_0 ) @ ( esk5_1 @ epred2_0 ) )
| ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_13]) ).
thf(c_0_18,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred2_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,negated_conjecture,
epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_13]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,negated_conjecture,
epred2_0 @ ( esk6_1 @ epred2_0 ) @ ( esk7_1 @ epred2_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) )
| ~ ( X1 @ ( esk3_1 @ X1 ) @ ( esk5_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 @ ( esk4_1 @ epred2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_20]),c_0_13]),c_0_21])]) ).
thf(c_0_24,negated_conjecture,
~ ( epred2_0 @ ( esk3_1 @ epred2_0 ) @ ( esk4_1 @ epred2_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_21])]),c_0_13]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk3_1 @ X1 ) @ ( esk4_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk6_1 @ X1 ) @ ( esk7_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_21])]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU462^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:42:00 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 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.HpAnPgYVjk/E---3.1_4008544.p
% 0.06/0.25 % Version: 3.5.1-ho
% 0.06/0.25 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.06/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.25 % Starting sh5l with 300s (1) cores
% 0.06/0.25 % Starting new_bool_1 with 300s (1) cores
% 0.06/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.06/0.25 % sh5l with pid 4008558 completed with status 0
% 0.06/0.25 % Result found by sh5l
% 0.06/0.25 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.06/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.25 % Starting sh5l with 300s (1) cores
% 0.06/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.06/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.06/0.25 % Search class: HGUNF-FFSF11-SHSSMMBN
% 0.06/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.25 % SubtermCWHack with pid 4008561 completed with status 0
% 0.06/0.25 % Result found by SubtermCWHack
% 0.06/0.25 % Preprocessing class: HSMSSMSSMLSNHSA.
% 0.06/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.06/0.25 % Starting sh5l with 300s (1) cores
% 0.06/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.06/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.06/0.25 % Search class: HGUNF-FFSF11-SHSSMMBN
% 0.06/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.06/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.06/0.25 % Preprocessing time : 0.001 s
% 0.06/0.25
% 0.06/0.25 % Proof found!
% 0.06/0.25 % SZS status Theorem
% 0.06/0.25 % SZS output start CNFRefutation
% See solution above
% 0.06/0.25 % Parsed axioms : 59
% 0.06/0.25 % Removed by relevancy pruning/SinE : 35
% 0.06/0.25 % Initial clauses : 9
% 0.06/0.25 % Removed in clause preprocessing : 0
% 0.06/0.25 % Initial clauses in saturation : 9
% 0.06/0.25 % Processed clauses : 23
% 0.06/0.25 % ...of these trivial : 0
% 0.06/0.25 % ...subsumed : 0
% 0.06/0.25 % ...remaining for further processing : 23
% 0.06/0.25 % Other redundant clauses eliminated : 0
% 0.06/0.25 % Clauses deleted for lack of memory : 0
% 0.06/0.25 % Backward-subsumed : 1
% 0.06/0.25 % Backward-rewritten : 3
% 0.06/0.25 % Generated clauses : 26
% 0.06/0.25 % ...of the previous two non-redundant : 22
% 0.06/0.25 % ...aggressively subsumed : 0
% 0.06/0.25 % Contextual simplify-reflections : 1
% 0.06/0.25 % Paramodulations : 26
% 0.06/0.25 % Factorizations : 0
% 0.06/0.25 % NegExts : 0
% 0.06/0.25 % Equation resolutions : 0
% 0.06/0.25 % Disequality decompositions : 0
% 0.06/0.25 % Total rewrite steps : 9
% 0.06/0.25 % ...of those cached : 7
% 0.06/0.25 % Propositional unsat checks : 0
% 0.06/0.25 % Propositional check models : 0
% 0.06/0.25 % Propositional check unsatisfiable : 0
% 0.06/0.25 % Propositional clauses : 0
% 0.06/0.25 % Propositional clauses after purity: 0
% 0.06/0.25 % Propositional unsat core size : 0
% 0.06/0.25 % Propositional preprocessing time : 0.000
% 0.06/0.25 % Propositional encoding time : 0.000
% 0.06/0.25 % Propositional solver time : 0.000
% 0.06/0.25 % Success case prop preproc time : 0.000
% 0.06/0.25 % Success case prop encoding time : 0.000
% 0.06/0.25 % Success case prop solver time : 0.000
% 0.06/0.25 % Current number of processed clauses : 19
% 0.06/0.25 % Positive orientable unit clauses : 2
% 0.06/0.25 % Positive unorientable unit clauses: 0
% 0.06/0.25 % Negative unit clauses : 2
% 0.06/0.25 % Non-unit-clauses : 15
% 0.06/0.25 % Current number of unprocessed clauses: 7
% 0.06/0.25 % ...number of literals in the above : 23
% 0.06/0.25 % Current number of archived formulas : 0
% 0.06/0.25 % Current number of archived clauses : 4
% 0.06/0.25 % Clause-clause subsumption calls (NU) : 32
% 0.06/0.25 % Rec. Clause-clause subsumption calls : 29
% 0.06/0.25 % Non-unit clause-clause subsumptions : 2
% 0.06/0.25 % Unit Clause-clause subsumption calls : 1
% 0.06/0.25 % Rewrite failures with RHS unbound : 0
% 0.06/0.25 % BW rewrite match attempts : 1
% 0.06/0.25 % BW rewrite match successes : 1
% 0.06/0.25 % Condensation attempts : 0
% 0.06/0.25 % Condensation successes : 0
% 0.06/0.25 % Termbank termtop insertions : 3767
% 0.06/0.25 % Search garbage collected termcells : 1012
% 0.06/0.25
% 0.06/0.25 % -------------------------------------------------
% 0.06/0.25 % User time : 0.006 s
% 0.06/0.25 % System time : 0.002 s
% 0.06/0.25 % Total time : 0.008 s
% 0.06/0.25 % Maximum resident set size: 4200 pages
% 0.06/0.25
% 0.06/0.25 % -------------------------------------------------
% 0.06/0.25 % User time : 0.009 s
% 0.06/0.25 % System time : 0.005 s
% 0.06/0.25 % Total time : 0.014 s
% 0.06/0.25 % Maximum resident set size: 4864 pages
% 0.06/0.25 % E exiting
%------------------------------------------------------------------------------