%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO062^4.002 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:42:15 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 16 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 286 ( 42 ~; 33 |; 5 &; 192 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 31 ^; 49 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
irel: $i > $i > $o ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_29,type,
iatom: ( $i > $o ) > $i > $o ).
thf(decl_30,type,
inot: ( $i > $o ) > $i > $o ).
thf(decl_34,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
a: $i > $o ).
thf(decl_44,type,
esk1_0: $i ).
thf(decl_45,type,
esk2_1: $i > $i ).
thf(decl_46,type,
esk3_1: $i > $i ).
thf(decl_47,type,
esk4_1: $i > $i ).
thf(inot,axiom,
( inot
= ( ^ [X12: $i > $o] : ( mnot @ ( mbox_s4 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',inot) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',mnot) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',mbox_s4) ).
thf(ior,axiom,
( ior
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mor @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',ior) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',mor) ).
thf(con,conjecture,
ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',con) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',ivalid) ).
thf(trans_axiom,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',trans_axiom) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/tmp/tmp.KEksqMaRJF/E---3.1_1501905.p',refl_axiom) ).
thf(c_0_10,plain,
( inot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X20: $i] :
( ( irel @ Z1 @ X20 )
=> ( Z0 @ X20 ) ) ) ),
inference(fof_simplification,[status(thm)],[inot]) ).
thf(c_0_11,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_12,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X2: $i] :
( ( irel @ Z1 @ X2 )
=> ( Z0 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_13,plain,
( ior
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ! [X22: $i] :
( ( irel @ Z2 @ X22 )
=> ( Z0 @ X22 ) )
| ! [X23: $i] :
( ( irel @ Z2 @ X23 )
=> ( Z1 @ X23 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ior]) ).
thf(c_0_14,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_15,negated_conjecture,
~ ( ivalid @ ( inot @ ( inot @ ( ior @ ( iatom @ a ) @ ( inot @ ( iatom @ a ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_16,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_17,plain,
( inot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X20: $i] :
( ( irel @ Z1 @ X20 )
=> ( Z0 @ X20 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_18,plain,
( ior
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ! [X22: $i] :
( ( irel @ Z2 @ X22 )
=> ( Z0 @ X22 ) )
| ! [X23: $i] :
( ( irel @ Z2 @ X23 )
=> ( Z1 @ X23 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_12]) ).
thf(c_0_19,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_20,negated_conjecture,
~ ! [X42: $i] :
~ ! [X41: $i] :
( ( irel @ X42 @ X41 )
=> ~ ! [X40: $i] :
( ( irel @ X41 @ X40 )
=> ( ! [X38: $i] :
( ( irel @ X40 @ X38 )
=> ( a @ X38 ) )
| ! [X39: $i] :
( ( irel @ X40 @ X39 )
=> ~ ! [X37: $i] :
( ( irel @ X39 @ X37 )
=> ( a @ X37 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_21,plain,
! [X44: $i,X45: $i,X46: $i] :
( ~ ( irel @ X44 @ X45 )
| ~ ( irel @ X45 @ X46 )
| ( irel @ X44 @ X46 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_22,negated_conjecture,
! [X48: $i,X52: $i] :
( ( ( irel @ X48 @ ( esk2_1 @ X48 ) )
| ~ ( irel @ esk1_0 @ X48 ) )
& ( ( irel @ ( esk2_1 @ X48 ) @ ( esk3_1 @ X48 ) )
| ~ ( irel @ esk1_0 @ X48 ) )
& ( ~ ( a @ ( esk3_1 @ X48 ) )
| ~ ( irel @ esk1_0 @ X48 ) )
& ( ( irel @ ( esk2_1 @ X48 ) @ ( esk4_1 @ X48 ) )
| ~ ( irel @ esk1_0 @ X48 ) )
& ( ~ ( irel @ ( esk4_1 @ X48 ) @ X52 )
| ( a @ X52 )
| ~ ( irel @ esk1_0 @ X48 ) ) ),
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_20])])])])])]) ).
thf(c_0_23,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( irel @ ( esk2_1 @ X1 ) @ ( esk3_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( irel @ ( esk2_1 @ X1 ) @ ( esk4_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X2: $i,X1: $i] :
( ( a @ X2 )
| ~ ( irel @ ( esk4_1 @ X1 ) @ X2 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_27,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk3_1 @ X2 ) )
| ~ ( irel @ X1 @ ( esk2_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ~ ( a @ ( esk3_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk4_1 @ X2 ) )
| ~ ( irel @ X1 @ ( esk2_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( irel @ ( esk4_1 @ X1 ) @ ( esk2_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( irel @ esk1_0 @ X2 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ ( esk4_1 @ X2 ) )
| ~ ( irel @ X3 @ ( esk2_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X2 )
| ~ ( irel @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i] :
( ~ ( irel @ esk1_0 @ ( esk4_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_34,negated_conjecture,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk4_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X2 )
| ~ ( irel @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
thf(c_0_35,plain,
! [X43: $i] : ( irel @ X43 @ X43 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i] :
~ ( irel @ esk1_0 @ X1 ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_37,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_38,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_36,c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO062^4.002 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n002.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:28:52 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.KEksqMaRJF/E---3.1_1501905.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.25 % Starting sh1l with 300s (1) cores
% 0.09/0.25 % Starting post_as_ho10 with 300s (1) cores
% 0.09/0.25 % post_as_ho1 with pid 1501919 completed with status 0
% 0.09/0.25 % Result found by post_as_ho1
% 0.09/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HHHNF-FFSF11-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 1501922 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_9 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HHHNF-FFSF11-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 : 43
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 28
% 0.09/0.25 % Removed in clause preprocessing : 21
% 0.09/0.25 % Initial clauses in saturation : 7
% 0.09/0.25 % Processed clauses : 24
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 4
% 0.09/0.25 % ...remaining for further processing : 20
% 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 : 17
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 44
% 0.09/0.25 % ...of the previous two non-redundant : 42
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 1
% 0.09/0.25 % Paramodulations : 44
% 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: 25
% 0.09/0.25 % ...number of literals in the above : 108
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 17
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 101
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 94
% 0.09/0.25 % Non-unit clause-clause subsumptions : 6
% 0.09/0.25 % Unit Clause-clause subsumption calls : 16
% 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 : 2633
% 0.09/0.25 % Search garbage collected termcells : 573
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.006 s
% 0.09/0.25 % System time : 0.001 s
% 0.09/0.25 % Total time : 0.008 s
% 0.09/0.25 % Maximum resident set size: 3608 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.007 s
% 0.09/0.25 % System time : 0.007 s
% 0.09/0.25 % Total time : 0.015 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------