%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO482^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:43:13 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 48 ( 17 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 57 ( 15 ~; 3 |; 1 &; 38 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 30 ^; 14 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_23,type,
meq_ind: mu > mu > $i > $o ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_34,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_s5: $i > $i > $o ).
thf(decl_55,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
esk1_0: $i ).
thf(decl_58,type,
esk2_0: mu ).
thf(decl_59,type,
esk3_0: $i ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [X11: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X11 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',mexists_ind) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',mnot) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X8: mu > $i > $o,X3: $i] :
! [X1: mu] : ( X8 @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',mforall_ind) ).
thf(prove,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X1: mu] :
( mbox_s5
@ ( mexists_ind
@ ^ [X2: mu] : ( meq_ind @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',prove) ).
thf(meq_ind,axiom,
( meq_ind
= ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',meq_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',mvalid) ).
thf(mbox_s5,axiom,
( mbox_s5
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7PAzW7S9K5/E---3.1_2393922.p',mbox_s5) ).
thf(c_0_7,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mexists_ind]) ).
thf(c_0_8,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_9,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X1: mu] : ( Z0 @ X1 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_10,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X1: mu] :
( mbox_s5
@ ( mexists_ind
@ ^ [X2: mu] : ( meq_ind @ X1 @ X2 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_11,plain,
( meq_ind
= ( ^ [Z0: mu,Z1: mu,Z2: $i] : Z0 ) ),
inference(fof_simplification,[status(thm)],[meq_ind]) ).
thf(c_0_12,plain,
( mexists_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
~ ! [X18: mu] :
~ ( Z0 @ X18 @ Z1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_13,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_14,plain,
( mbox_s5
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s5]) ).
thf(c_0_15,negated_conjecture,
~ ! [X31: $i,X30: mu,X29: $i] :
( ~ ( rel_s5 @ X31 @ X29 )
| ~ ! [X28: mu] : ( X30 != X28 ) ),
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_10]),c_0_11]),c_0_9]),c_0_12]),c_0_13]),c_0_14])]) ).
thf(c_0_16,negated_conjecture,
! [X41: mu] :
( ( rel_s5 @ esk1_0 @ esk3_0 )
& ( esk2_0 != X41 ) ),
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_15])])])])]) ).
thf(c_0_17,negated_conjecture,
! [X1: mu] : ( esk2_0 != X1 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO482^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.16 % Computer : n013.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.16 % CPULimit : 300
% 0.12/0.16 % WCLimit : 300
% 0.12/0.16 % DateTime : Tue Sep 29 17:08:06 UTC 2026
% 0.12/0.16 % CPUTime :
% 0.12/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running higher-order theorem proving
% 0.12/0.22 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.7PAzW7S9K5/E---3.1_2393922.p
% 0.12/0.24 % Version: 3.5.1-ho
% 0.12/0.24 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.24 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.24 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.24 % Starting almost_fo_3_lam with 300s (1) cores
% 0.12/0.24 % Starting post_as_ho1 with 300s (1) cores
% 0.12/0.24 % ho_unfolding_3 with pid 2393936 completed with status 0
% 0.12/0.24 % Result found by ho_unfolding_3
% 0.12/0.24 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.24 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.24 % No SInE strategy applied
% 0.12/0.24 % Search class: HHUSF-FFSF00-SHSSMFNN
% 0.12/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.24 % Starting ho_unfolding_3 with 151s (1) cores
% 0.12/0.24 % Starting sh5l with 136s (1) cores
% 0.12/0.24 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.24 % Starting new_bool_2 with 136s (1) cores
% 0.12/0.24 % sh5l with pid 2393942 completed with status 0
% 0.12/0.24 % Result found by sh5l
% 0.12/0.24 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.12/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.24 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.12/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.24 % No SInE strategy applied
% 0.12/0.24 % Search class: HHUSF-FFSF00-SHSSMFNN
% 0.12/0.24 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.24 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.24 % Starting ho_unfolding_3 with 151s (1) cores
% 0.12/0.24 % Starting sh5l with 136s (1) cores
% 0.12/0.24 % Preprocessing time : 0.001 s
% 0.12/0.24 % Presaturation interreduction done
% 0.12/0.24
% 0.12/0.24 % Proof found!
% 0.12/0.24 % SZS status Theorem
% 0.12/0.24 % SZS output start CNFRefutation
% See solution above
% 0.12/0.24 % Parsed axioms : 72
% 0.12/0.24 % Removed by relevancy pruning/SinE : 0
% 0.12/0.24 % Initial clauses : 40
% 0.12/0.24 % Removed in clause preprocessing : 35
% 0.12/0.24 % Initial clauses in saturation : 5
% 0.12/0.24 % Processed clauses : 1
% 0.12/0.24 % ...of these trivial : 0
% 0.12/0.24 % ...subsumed : 0
% 0.12/0.24 % ...remaining for further processing : 1
% 0.12/0.24 % Other redundant clauses eliminated : 1
% 0.12/0.24 % Clauses deleted for lack of memory : 0
% 0.12/0.24 % Backward-subsumed : 0
% 0.12/0.24 % Backward-rewritten : 0
% 0.12/0.24 % Generated clauses : 1
% 0.12/0.24 % ...of the previous two non-redundant : 0
% 0.12/0.24 % ...aggressively subsumed : 0
% 0.12/0.24 % Contextual simplify-reflections : 0
% 0.12/0.24 % Paramodulations : 0
% 0.12/0.24 % Factorizations : 0
% 0.12/0.24 % NegExts : 0
% 0.12/0.24 % Equation resolutions : 1
% 0.12/0.24 % Disequality decompositions : 0
% 0.12/0.24 % Total rewrite steps : 0
% 0.12/0.24 % ...of those cached : 0
% 0.12/0.24 % Propositional unsat checks : 0
% 0.12/0.24 % Propositional check models : 0
% 0.12/0.24 % Propositional check unsatisfiable : 0
% 0.12/0.24 % Propositional clauses : 0
% 0.12/0.24 % Propositional clauses after purity: 0
% 0.12/0.24 % Propositional unsat core size : 0
% 0.12/0.24 % Propositional preprocessing time : 0.000
% 0.12/0.24 % Propositional encoding time : 0.000
% 0.12/0.24 % Propositional solver time : 0.000
% 0.12/0.24 % Success case prop preproc time : 0.000
% 0.12/0.24 % Success case prop encoding time : 0.000
% 0.12/0.24 % Success case prop solver time : 0.000
% 0.12/0.24 % Current number of processed clauses : 0
% 0.12/0.24 % Positive orientable unit clauses : 0
% 0.12/0.24 % Positive unorientable unit clauses: 0
% 0.12/0.24 % Negative unit clauses : 0
% 0.12/0.24 % Non-unit-clauses : 0
% 0.12/0.24 % Current number of unprocessed clauses: 4
% 0.12/0.24 % ...number of literals in the above : 7
% 0.12/0.24 % Current number of archived formulas : 0
% 0.12/0.24 % Current number of archived clauses : 0
% 0.12/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.24 % Non-unit clause-clause subsumptions : 0
% 0.12/0.24 % Unit Clause-clause subsumption calls : 0
% 0.12/0.24 % Rewrite failures with RHS unbound : 0
% 0.12/0.24 % BW rewrite match attempts : 0
% 0.12/0.24 % BW rewrite match successes : 0
% 0.12/0.24 % Condensation attempts : 1
% 0.12/0.24 % Condensation successes : 0
% 0.12/0.24 % Termbank termtop insertions : 2315
% 0.12/0.24 % Search garbage collected termcells : 449
% 0.12/0.24
% 0.12/0.24 % -------------------------------------------------
% 0.12/0.24 % User time : 0.001 s
% 0.12/0.24 % System time : 0.004 s
% 0.12/0.24 % Total time : 0.004 s
% 0.12/0.24 % Maximum resident set size: 3700 pages
% 0.12/0.24
% 0.12/0.24 % -------------------------------------------------
% 0.12/0.24 % User time : 0.005 s
% 0.12/0.24 % System time : 0.012 s
% 0.12/0.24 % Total time : 0.017 s
% 0.12/0.24 % Maximum resident set size: 4608 pages
% 0.12/0.24 % E exiting
%------------------------------------------------------------------------------