%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO572^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:43:26 AM UTC 2026
% Result : Theorem 0.24s 0.29s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 19 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 209 ( 41 ~; 22 |; 3 &; 136 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 43 ^; 35 !; 1 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
exists_in_world: mu > $i > $o ).
thf(decl_38,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_39,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_55,type,
rel_s4: $i > $i > $o ).
thf(decl_56,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(decl_58,type,
f: mu > $i > $o ).
thf(decl_59,type,
esk1_1: $i > mu ).
thf(decl_60,type,
esk2_0: $i ).
thf(decl_61,type,
esk3_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mor) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X13: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X14: mu] : ( mnot @ ( X13 @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mexists_ind) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ X3 )
=> ( X11 @ X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mforall_ind) ).
thf(mdia_s4,axiom,
( mdia_s4
= ( ^ [X4: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mdia_s4) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mbox_s4) ).
thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mdia_s4
@ ( mforall_ind
@ ^ [X20: mu] : ( f @ X20 ) ) )
@ ( mexists_ind
@ ^ [X21: mu] : ( mdia_s4 @ ( f @ X21 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',con) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',mvalid) ).
thf(cumulative_ax,axiom,
! [X19: mu,X7: $i,X3: $i] :
( ( ( exists_in_world @ X19 @ X7 )
& ( rel_s4 @ X7 @ X3 ) )
=> ( exists_in_world @ X19 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',cumulative_ax) ).
thf(nonempty_ax,axiom,
! [X7: $i] :
? [X10: mu] : ( exists_in_world @ X10 @ X7 ),
file('/export/starexec/sandbox2/tmp/tmp.mHYxrvSbGq/E---3.1_1100424.p',nonempty_ax) ).
thf(c_0_11,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_12,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_13,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_14,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X28: mu] :
( ( exists_in_world @ X28 @ Z1 )
=> ~ ( Z0 @ X28 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_15,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ Z1 )
=> ( Z0 @ X12 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_16,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X30: $i] :
( ~ ( rel_s4 @ Z1 @ X30 )
| ~ ( Z0 @ X30 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_s4]) ).
thf(c_0_17,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ Z1 @ X7 )
| ( Z0 @ X7 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_18,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mdia_s4
@ ( mforall_ind
@ ^ [X20: mu] : ( f @ X20 ) ) )
@ ( mexists_ind
@ ^ [X21: mu] : ( mdia_s4 @ ( f @ X21 ) ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_19,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_11,c_0_12]),c_0_13]) ).
thf(c_0_20,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X28: mu] :
( ( exists_in_world @ X28 @ Z1 )
=> ~ ( Z0 @ X28 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_12]),c_0_15]) ).
thf(c_0_21,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_22,plain,
( mdia_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X30: $i] :
( ~ ( rel_s4 @ Z1 @ X30 )
| ~ ( Z0 @ X30 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_12]),c_0_17]) ).
thf(c_0_23,negated_conjecture,
~ ! [X39: $i] :
( ~ ~ ! [X36: $i] :
( ~ ( rel_s4 @ X39 @ X36 )
| ~ ! [X35: mu] :
( ( exists_in_world @ X35 @ X36 )
=> ( f @ X35 @ X36 ) ) )
| ~ ! [X38: mu] :
( ( exists_in_world @ X38 @ X39 )
=> ~ ~ ! [X37: $i] :
( ~ ( rel_s4 @ X39 @ X37 )
| ~ ( f @ X38 @ X37 ) ) ) ),
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_18]),c_0_19]),c_0_15]),c_0_20]),c_0_21]),c_0_22])]) ).
thf(c_0_24,plain,
! [X46: mu,X47: $i,X48: $i] :
( ~ ( exists_in_world @ X46 @ X47 )
| ~ ( rel_s4 @ X47 @ X48 )
| ( exists_in_world @ X46 @ X48 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cumulative_ax])])]) ).
thf(c_0_25,negated_conjecture,
! [X51: mu,X52: mu,X53: $i] :
( ( rel_s4 @ esk2_0 @ esk3_0 )
& ( ~ ( exists_in_world @ X51 @ esk3_0 )
| ( f @ X51 @ esk3_0 ) )
& ( ~ ( exists_in_world @ X52 @ esk2_0 )
| ~ ( rel_s4 @ esk2_0 @ X53 )
| ~ ( f @ X52 @ X53 ) ) ),
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_23])])])])]) ).
thf(c_0_26,plain,
! [X3: $i,X10: mu,X7: $i] :
( ( exists_in_world @ X10 @ X7 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( rel_s4 @ X3 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_27,negated_conjecture,
rel_s4 @ esk2_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
! [X10: mu,X3: $i] :
( ~ ( exists_in_world @ X10 @ esk2_0 )
| ~ ( rel_s4 @ esk2_0 @ X3 )
| ~ ( f @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X10: mu] :
( ( f @ X10 @ esk3_0 )
| ~ ( exists_in_world @ X10 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,negated_conjecture,
! [X10: mu] :
( ( exists_in_world @ X10 @ esk3_0 )
| ~ ( exists_in_world @ X10 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
thf(c_0_31,plain,
! [X40: $i] : ( exists_in_world @ ( esk1_1 @ X40 ) @ X40 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[nonempty_ax])]) ).
thf(c_0_32,negated_conjecture,
! [X10: mu] :
~ ( exists_in_world @ X10 @ esk2_0 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_27])]),c_0_30]) ).
thf(c_0_33,plain,
! [X3: $i] : ( exists_in_world @ ( esk1_1 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_34,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_32,c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO572^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n019.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:15:32 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.08/0.27 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.mHYxrvSbGq/E---3.1_1100424.p
% 0.24/0.29 % Version: 3.5.1-ho
% 0.24/0.29 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.29 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.24/0.29 % Starting almost_fo_3_lam with 300s (1) cores
% 0.24/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.29 % ehoh_best2_full_lfho with pid 1100438 completed with status 0
% 0.24/0.29 % Result found by ehoh_best2_full_lfho
% 0.24/0.29 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.29 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.24/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.29 % No SInE strategy applied
% 0.24/0.29 % Search class: HHHNS-FFSF11-SHSSMFNN
% 0.24/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.29 % SubtermCWHack with pid 1100442 completed with status 0
% 0.24/0.29 % Result found by SubtermCWHack
% 0.24/0.29 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.24/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.24/0.29 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.24/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.29 % No SInE strategy applied
% 0.24/0.29 % Search class: HHHNS-FFSF11-SHSSMFNN
% 0.24/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.29 % Preprocessing time : 0.001 s
% 0.24/0.29
% 0.24/0.29 % Proof found!
% 0.24/0.29 % SZS status Theorem
% 0.24/0.29 % SZS output start CNFRefutation
% See solution above
% 0.24/0.30 % Parsed axioms : 74
% 0.24/0.30 % Removed by relevancy pruning/SinE : 0
% 0.24/0.30 % Initial clauses : 44
% 0.24/0.30 % Removed in clause preprocessing : 37
% 0.24/0.30 % Initial clauses in saturation : 7
% 0.24/0.30 % Processed clauses : 10
% 0.24/0.30 % ...of these trivial : 0
% 0.24/0.30 % ...subsumed : 0
% 0.24/0.30 % ...remaining for further processing : 10
% 0.24/0.30 % Other redundant clauses eliminated : 0
% 0.24/0.30 % Clauses deleted for lack of memory : 0
% 0.24/0.30 % Backward-subsumed : 2
% 0.24/0.30 % Backward-rewritten : 0
% 0.24/0.30 % Generated clauses : 8
% 0.24/0.30 % ...of the previous two non-redundant : 5
% 0.24/0.30 % ...aggressively subsumed : 0
% 0.24/0.30 % Contextual simplify-reflections : 1
% 0.24/0.30 % Paramodulations : 8
% 0.24/0.30 % Factorizations : 0
% 0.24/0.30 % NegExts : 0
% 0.24/0.30 % Equation resolutions : 0
% 0.24/0.30 % Disequality decompositions : 0
% 0.24/0.30 % Total rewrite steps : 1
% 0.24/0.30 % ...of those cached : 0
% 0.24/0.30 % Propositional unsat checks : 0
% 0.24/0.30 % Propositional check models : 0
% 0.24/0.30 % Propositional check unsatisfiable : 0
% 0.24/0.30 % Propositional clauses : 0
% 0.24/0.30 % Propositional clauses after purity: 0
% 0.24/0.30 % Propositional unsat core size : 0
% 0.24/0.30 % Propositional preprocessing time : 0.000
% 0.24/0.30 % Propositional encoding time : 0.000
% 0.24/0.30 % Propositional solver time : 0.000
% 0.24/0.30 % Success case prop preproc time : 0.000
% 0.24/0.30 % Success case prop encoding time : 0.000
% 0.24/0.30 % Success case prop solver time : 0.000
% 0.24/0.30 % Current number of processed clauses : 8
% 0.24/0.30 % Positive orientable unit clauses : 3
% 0.24/0.30 % Positive unorientable unit clauses: 0
% 0.24/0.30 % Negative unit clauses : 1
% 0.24/0.30 % Non-unit-clauses : 4
% 0.24/0.30 % Current number of unprocessed clauses: 2
% 0.24/0.30 % ...number of literals in the above : 6
% 0.24/0.30 % Current number of archived formulas : 0
% 0.24/0.30 % Current number of archived clauses : 2
% 0.24/0.30 % Clause-clause subsumption calls (NU) : 1
% 0.24/0.30 % Rec. Clause-clause subsumption calls : 1
% 0.24/0.30 % Non-unit clause-clause subsumptions : 1
% 0.24/0.30 % Unit Clause-clause subsumption calls : 2
% 0.24/0.30 % Rewrite failures with RHS unbound : 0
% 0.24/0.30 % BW rewrite match attempts : 1
% 0.24/0.30 % BW rewrite match successes : 0
% 0.24/0.30 % Condensation attempts : 0
% 0.24/0.30 % Condensation successes : 0
% 0.24/0.30 % Termbank termtop insertions : 2770
% 0.24/0.30 % Search garbage collected termcells : 585
% 0.24/0.30
% 0.24/0.30 % -------------------------------------------------
% 0.24/0.30 % User time : 0.005 s
% 0.24/0.30 % System time : 0.003 s
% 0.24/0.30 % Total time : 0.008 s
% 0.24/0.30 % Maximum resident set size: 3652 pages
% 0.24/0.30
% 0.24/0.30 % -------------------------------------------------
% 0.24/0.30 % User time : 0.007 s
% 0.24/0.30 % System time : 0.009 s
% 0.24/0.30 % Total time : 0.016 s
% 0.24/0.30 % Maximum resident set size: 4864 pages
% 0.24/0.30 % E exiting
%------------------------------------------------------------------------------