%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KRS275^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:11:53 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 18 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 236 ( 42 ~; 20 |; 5 &; 163 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 68 ( 39 ^; 29 !; 0 ?; 68 :)
% 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_31,type,
mand: ( $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_41,type,
mreflexive: ( $i > $i > $o ) > $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_58,type,
teach: mu > mu > $i > $o ).
thf(decl_59,type,
sue: mu ).
thf(decl_60,type,
psych: mu ).
thf(decl_61,type,
mary: mu ).
thf(decl_62,type,
cs: mu ).
thf(decl_63,type,
math: mu ).
thf(decl_64,type,
john: mu ).
thf(decl_66,type,
esk2_2: $i > $i > mu ).
thf(decl_67,type,
esk3_0: $i ).
thf(decl_68,type,
esk4_1: mu > $i ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mor) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X13: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X14: mu] : ( mnot @ ( X13 @ X14 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.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/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mvalid) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mbox_s4) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X6: $i > $i > $o] :
! [X16: $i] : ( X6 @ X16 @ X16 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',mreflexive) ).
thf(query,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( teach @ john @ X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',query) ).
thf(db,axiom,
( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [X20: mu] : ( teach @ X20 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',db) ).
thf(a1,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',a1) ).
thf(existence_of_math_ax,axiom,
! [X7: $i] : ( exists_in_world @ math @ X7 ),
file('/export/starexec/sandbox/tmp/tmp.SK6fPLNbN0/E---3.1_2570838.p',existence_of_math_ax) ).
thf(c_0_12,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_13,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
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,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X34: mu] :
( ( exists_in_world @ X34 @ Z1 )
=> ~ ( Z0 @ X34 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_16,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_17,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_18,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X34: mu] :
( ( exists_in_world @ X34 @ Z1 )
=> ~ ( Z0 @ X34 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_15,c_0_13]),c_0_16]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,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_21,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X16: $i] : ( Z0 @ X16 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_22,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X21: mu] : ( mbox_s4 @ ( teach @ john @ X21 ) ) ) ),
inference(assume_negation,[status(cth)],[query]) ).
thf(c_0_23,plain,
! [X43: $i,X42: $i] :
( ~ ( rel_s4 @ X43 @ X42 )
| ~ ( ~ ( teach @ john @ math @ X42 )
| ~ ~ ( ~ ~ ! [X41: mu] :
( ( exists_in_world @ X41 @ X42 )
=> ~ ( teach @ X41 @ cs @ X42 ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X42 )
| ~ ( teach @ sue @ psych @ X42 ) ) ) ) ),
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(fof_simplification,[status(thm)],[db]),c_0_17]),c_0_18]),c_0_19]),c_0_20])]) ).
thf(c_0_24,plain,
! [X37: $i] : ( rel_s4 @ X37 @ X37 ),
inference(apply_def,[status(thm)],[a1,c_0_21]) ).
thf(c_0_25,negated_conjecture,
~ ! [X46: $i] :
~ ! [X45: mu] :
( ( exists_in_world @ X45 @ X46 )
=> ~ ! [X44: $i] :
( ~ ( rel_s4 @ X46 @ X44 )
| ( teach @ john @ X45 @ X44 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_22]),c_0_18]),c_0_19]),c_0_20])]) ).
thf(c_0_26,plain,
! [X62: $i,X63: $i] :
( ( ( teach @ john @ math @ X63 )
| ~ ( rel_s4 @ X62 @ X63 ) )
& ( ( exists_in_world @ ( esk2_2 @ X62 @ X63 ) @ X63 )
| ~ ( rel_s4 @ X62 @ X63 ) )
& ( ( teach @ ( esk2_2 @ X62 @ X63 ) @ cs @ X63 )
| ~ ( rel_s4 @ X62 @ X63 ) )
& ( ( teach @ mary @ psych @ X63 )
| ~ ( rel_s4 @ X62 @ X63 ) )
& ( ( teach @ sue @ psych @ X63 )
| ~ ( rel_s4 @ X62 @ X63 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])]) ).
thf(c_0_27,plain,
! [X49: $i] : ( rel_s4 @ X49 @ X49 ),
inference(variable_rename,[status(thm)],[c_0_24]) ).
thf(c_0_28,negated_conjecture,
! [X66: mu] :
( ( ( rel_s4 @ esk3_0 @ ( esk4_1 @ X66 ) )
| ~ ( exists_in_world @ X66 @ esk3_0 ) )
& ( ~ ( teach @ john @ X66 @ ( esk4_1 @ X66 ) )
| ~ ( exists_in_world @ X66 @ esk3_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
thf(c_0_29,plain,
! [X7: $i,X3: $i] :
( ( teach @ john @ math @ X3 )
| ~ ( rel_s4 @ X7 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_30,plain,
! [X3: $i] : ( rel_s4 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_31,plain,
! [X60: $i] : ( exists_in_world @ math @ X60 ),
inference(variable_rename,[status(thm)],[existence_of_math_ax]) ).
thf(c_0_32,negated_conjecture,
! [X10: mu] :
( ~ ( teach @ john @ X10 @ ( esk4_1 @ X10 ) )
| ~ ( exists_in_world @ X10 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,plain,
! [X3: $i] : ( teach @ john @ math @ X3 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_34,plain,
! [X3: $i] : ( exists_in_world @ math @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KRS275^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 % Computer : n010.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 08:42:18 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 Running higher-order theorem proving
% 0.22/0.28 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.SK6fPLNbN0/E---3.1_2570838.p
% 0.22/0.30 % Version: 3.5.1-ho
% 0.22/0.30 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.30 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.30 % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.30 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.30 % almost_fo_3_lam with pid 2570853 completed with status 0
% 0.22/0.30 % Result found by almost_fo_3_lam
% 0.22/0.30 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.30 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.30 % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HHHNM-FFSF21-SHSSMFNN
% 0.22/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30 % SubtermCWHack with pid 2570858 completed with status 0
% 0.22/0.30 % Result found by SubtermCWHack
% 0.22/0.30 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.22/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.30 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.22/0.30 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.22/0.30 % Starting almost_fo_3_lam with 300s (1) cores
% 0.22/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.30 % No SInE strategy applied
% 0.22/0.30 % Search class: HHHNM-FFSF21-SHSSMFNN
% 0.22/0.30 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.30 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.30 % Preprocessing time : 0.002 s
% 0.22/0.30
% 0.22/0.30 % Proof found!
% 0.22/0.30 % SZS status Theorem
% 0.22/0.30 % SZS output start CNFRefutation
% See solution above
% 0.22/0.31 % Parsed axioms : 87
% 0.22/0.31 % Removed by relevancy pruning/SinE : 0
% 0.22/0.31 % Initial clauses : 60
% 0.22/0.31 % Removed in clause preprocessing : 43
% 0.22/0.31 % Initial clauses in saturation : 17
% 0.22/0.31 % Processed clauses : 18
% 0.22/0.31 % ...of these trivial : 0
% 0.22/0.31 % ...subsumed : 0
% 0.22/0.31 % ...remaining for further processing : 18
% 0.22/0.31 % Other redundant clauses eliminated : 0
% 0.22/0.31 % Clauses deleted for lack of memory : 0
% 0.22/0.31 % Backward-subsumed : 0
% 0.22/0.31 % Backward-rewritten : 3
% 0.22/0.31 % Generated clauses : 9
% 0.22/0.31 % ...of the previous two non-redundant : 7
% 0.22/0.31 % ...aggressively subsumed : 0
% 0.22/0.31 % Contextual simplify-reflections : 0
% 0.22/0.31 % Paramodulations : 9
% 0.22/0.31 % Factorizations : 0
% 0.22/0.31 % NegExts : 0
% 0.22/0.31 % Equation resolutions : 0
% 0.22/0.31 % Disequality decompositions : 0
% 0.22/0.31 % Total rewrite steps : 4
% 0.22/0.31 % ...of those cached : 0
% 0.22/0.31 % Propositional unsat checks : 0
% 0.22/0.31 % Propositional check models : 0
% 0.22/0.31 % Propositional check unsatisfiable : 0
% 0.22/0.31 % Propositional clauses : 0
% 0.22/0.31 % Propositional clauses after purity: 0
% 0.22/0.31 % Propositional unsat core size : 0
% 0.22/0.31 % Propositional preprocessing time : 0.000
% 0.22/0.31 % Propositional encoding time : 0.000
% 0.22/0.31 % Propositional solver time : 0.000
% 0.22/0.31 % Success case prop preproc time : 0.000
% 0.22/0.31 % Success case prop encoding time : 0.000
% 0.22/0.31 % Success case prop solver time : 0.000
% 0.22/0.31 % Current number of processed clauses : 15
% 0.22/0.31 % Positive orientable unit clauses : 11
% 0.22/0.31 % Positive unorientable unit clauses: 0
% 0.22/0.31 % Negative unit clauses : 0
% 0.22/0.31 % Non-unit-clauses : 4
% 0.22/0.31 % Current number of unprocessed clauses: 6
% 0.22/0.31 % ...number of literals in the above : 14
% 0.22/0.31 % Current number of archived formulas : 0
% 0.22/0.31 % Current number of archived clauses : 3
% 0.22/0.31 % Clause-clause subsumption calls (NU) : 0
% 0.22/0.31 % Rec. Clause-clause subsumption calls : 0
% 0.22/0.31 % Non-unit clause-clause subsumptions : 0
% 0.22/0.31 % Unit Clause-clause subsumption calls : 0
% 0.22/0.31 % Rewrite failures with RHS unbound : 0
% 0.22/0.31 % BW rewrite match attempts : 3
% 0.22/0.31 % BW rewrite match successes : 3
% 0.22/0.31 % Condensation attempts : 0
% 0.22/0.31 % Condensation successes : 0
% 0.22/0.31 % Termbank termtop insertions : 3320
% 0.22/0.31 % Search garbage collected termcells : 710
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.005 s
% 0.22/0.31 % System time : 0.004 s
% 0.22/0.31 % Total time : 0.009 s
% 0.22/0.31 % Maximum resident set size: 3968 pages
% 0.22/0.31
% 0.22/0.31 % -------------------------------------------------
% 0.22/0.31 % User time : 0.007 s
% 0.22/0.31 % System time : 0.009 s
% 0.22/0.31 % Total time : 0.017 s
% 0.22/0.31 % Maximum resident set size: 4864 pages
% 0.22/0.31 % E exiting
%------------------------------------------------------------------------------