%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN041^4 : 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 : 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 08:40:49 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 19 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 260 ( 37 ~; 27 |; 8 &; 172 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 39 ^; 38 !; 0 ?; 77 :)
% 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_27,type,
mimplies: ( $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_35,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_43,type,
p: $i > $o ).
thf(decl_44,type,
q: $i > $o ).
thf(decl_45,type,
esk1_0: $i ).
thf(decl_46,type,
esk2_1: $i > $i ).
thf(decl_47,type,
esk3_1: $i > $i ).
thf(decl_48,type,
esk4_0: $i ).
thf(decl_49,type,
esk5_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',mor) ).
thf(inot,axiom,
( inot
= ( ^ [X12: $i > $o] : ( mnot @ ( mbox_s4 @ X12 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',inot) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',mbox_s4) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',iimplies) ).
thf(pel3,conjecture,
ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',pel3) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.p',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sjAFrUeHP5/E---3.1_278697.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.sjAFrUeHP5/E---3.1_278697.p',trans_axiom) ).
thf(c_0_10,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_11,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_12,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_13,plain,
( inot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X20: $i] :
( ( irel @ Z1 @ X20 )
=> ( Z0 @ X20 ) ) ) ),
inference(fof_simplification,[status(thm)],[inot]) ).
thf(c_0_14,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_15,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iimplies]) ).
thf(c_0_16,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_17,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( inot @ ( iimplies @ ( iatom @ p ) @ ( iatom @ q ) ) ) @ ( iimplies @ ( iatom @ q ) @ ( iatom @ p ) ) ) ),
inference(assume_negation,[status(cth)],[pel3]) ).
thf(c_0_18,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_19,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_13,c_0_11]),c_0_14]) ).
thf(c_0_20,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
thf(c_0_21,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_22,negated_conjecture,
~ ! [X44: $i] :
( ~ ! [X42: $i] :
( ( irel @ X44 @ X42 )
=> ~ ! [X39: $i] :
( ( irel @ X42 @ X39 )
=> ( ~ ! [X37: $i] :
( ( irel @ X39 @ X37 )
=> ( p @ X37 ) )
| ! [X38: $i] :
( ( irel @ X39 @ X38 )
=> ( q @ X38 ) ) ) ) )
| ! [X43: $i] :
( ( irel @ X44 @ X43 )
=> ( ~ ! [X40: $i] :
( ( irel @ X43 @ X40 )
=> ( q @ X40 ) )
| ! [X41: $i] :
( ( irel @ X43 @ X41 )
=> ( p @ X41 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X50: $i,X52: $i,X55: $i] :
( ( ( irel @ X50 @ ( esk2_1 @ X50 ) )
| ~ ( irel @ esk1_0 @ X50 ) )
& ( ~ ( irel @ ( esk2_1 @ X50 ) @ X52 )
| ( p @ X52 )
| ~ ( irel @ esk1_0 @ X50 ) )
& ( ( irel @ ( esk2_1 @ X50 ) @ ( esk3_1 @ X50 ) )
| ~ ( irel @ esk1_0 @ X50 ) )
& ( ~ ( q @ ( esk3_1 @ X50 ) )
| ~ ( irel @ esk1_0 @ X50 ) )
& ( irel @ esk1_0 @ esk4_0 )
& ( ~ ( irel @ esk4_0 @ X55 )
| ( q @ X55 ) )
& ( irel @ esk4_0 @ esk5_0 )
& ~ ( p @ esk5_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_22])])])])])]) ).
thf(c_0_24,plain,
! [X46: $i,X47: $i,X48: $i] :
( ~ ( irel @ X46 @ X47 )
| ~ ( irel @ X47 @ X48 )
| ( irel @ X46 @ X48 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ~ ( q @ ( esk3_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( q @ X1 )
| ~ ( irel @ esk4_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ( irel @ ( esk2_1 @ X1 ) @ ( esk3_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i] :
( ~ ( irel @ esk4_0 @ ( esk3_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,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_27,c_0_28]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i] :
( ~ ( irel @ esk4_0 @ ( esk2_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ ( esk2_1 @ X1 ) )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_33,negated_conjecture,
irel @ esk1_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN041^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 16:16:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.sjAFrUeHP5/E---3.1_278697.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.25 % Starting post_as_ho11 with 300s (1) cores
% 0.07/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.07/0.25 % new_ho_10_cnf2 with pid 278710 completed with status 0
% 0.07/0.25 % Result found by new_ho_10_cnf2
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.07/0.25 % Starting lpo1_def_fix with 136s (1) cores
% 0.07/0.25 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.07/0.25 % Starting new_ho_7 with 136s (1) cores
% 0.07/0.25 % lpo1_lambda_fix with pid 278717 completed with status 0
% 0.07/0.25 % Result found by lpo1_lambda_fix
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLSNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.07/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHNF-FFSF11-SHSSMFNN
% 0.07/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.25 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.07/0.25 % Starting lpo1_def_fix with 136s (1) cores
% 0.07/0.25 % Starting lpo1_lambda_fix with 136s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25 % Presaturation interreduction done
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 44
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 32
% 0.07/0.25 % Removed in clause preprocessing : 22
% 0.07/0.25 % Initial clauses in saturation : 10
% 0.07/0.25 % Processed clauses : 41
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 7
% 0.07/0.25 % ...remaining for further processing : 34
% 0.07/0.25 % Other redundant clauses eliminated : 0
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 28
% 0.07/0.25 % ...of the previous two non-redundant : 25
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 28
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 0
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 1
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 24
% 0.07/0.25 % Positive orientable unit clauses : 3
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 20
% 0.07/0.25 % Current number of unprocessed clauses: 4
% 0.07/0.25 % ...number of literals in the above : 16
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 10
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 74
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 64
% 0.07/0.25 % Non-unit clause-clause subsumptions : 7
% 0.07/0.25 % Unit Clause-clause subsumption calls : 0
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 9
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 2562
% 0.07/0.25 % Search garbage collected termcells : 680
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.002 s
% 0.07/0.25 % System time : 0.003 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3920 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.013 s
% 0.07/0.25 % System time : 0.012 s
% 0.07/0.25 % Total time : 0.025 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------