%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEG018^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 07:49:20 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 158 ( 18 equ; 0 cnn)
% Maximal formula atoms : 29 ( 6 avg)
% Number of connectives : 407 ( 46 ~; 24 |; 41 &; 264 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 106 ( 38 ^; 50 !; 18 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
reg: $tType ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
c: reg > reg > $o ).
thf(decl_56,type,
p: reg > reg > $o ).
thf(decl_58,type,
o: reg > reg > $o ).
thf(decl_60,type,
ec: reg > reg > $o ).
thf(decl_61,type,
pp: reg > reg > $o ).
thf(decl_63,type,
ntpp: reg > reg > $o ).
thf(decl_69,type,
fool: $i > $i > $o ).
thf(decl_70,type,
esk1_0: $i ).
thf(decl_71,type,
esk2_0: $i ).
thf(decl_72,type,
esk3_0: reg ).
thf(decl_73,type,
esk4_1: reg > reg ).
thf(decl_74,type,
esk5_2: reg > reg > reg ).
thf(decl_75,type,
esk6_2: reg > reg > reg ).
thf(o,axiom,
( o
= ( ^ [X28: reg,X29: reg] :
? [X25: reg] :
( ( p @ X25 @ X28 )
& ( p @ X25 @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',o) ).
thf(p,axiom,
( p
= ( ^ [X23: reg,X24: reg] :
! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ X24 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',p) ).
thf(pp,axiom,
( pp
= ( ^ [X34: reg,X35: reg] :
( ( p @ X34 @ X35 )
& ~ ( p @ X35 @ X34 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',pp) ).
thf(ec,axiom,
( ec
= ( ^ [X32: reg,X33: reg] :
( ( c @ X32 @ X33 )
& ~ ( o @ X32 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',ec) ).
thf(ntpp,axiom,
( ntpp
= ( ^ [X38: reg,X39: reg] :
( ( pp @ X38 @ X39 )
& ~ ? [X25: reg] :
( ( ec @ X25 @ X38 )
& ( ec @ X25 @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',ntpp) ).
thf(con,conjecture,
( mvalid
@ ( mbox @ fool
@ ^ [X44: $i] :
~ ? [X25: reg] :
! [X45: reg] : ( ntpp @ X25 @ X45 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',con) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8kCUMheGqD/E---3.1_1432889.p',mvalid) ).
thf(c_0_8,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X49: reg] :
( ( c @ X49 @ X25 )
=> ( c @ X49 @ Z0 ) )
& ! [X50: reg] :
( ( c @ X50 @ X25 )
=> ( c @ X50 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[o]) ).
thf(c_0_9,plain,
( p
= ( ^ [Z0: reg,Z1: reg] :
! [X25: reg] :
( ( c @ X25 @ Z0 )
=> ( c @ X25 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[p]) ).
thf(c_0_10,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X54: reg] :
( ( c @ X54 @ Z0 )
=> ( c @ X54 @ Z1 ) )
& ~ ! [X55: reg] :
( ( c @ X55 @ Z1 )
=> ( c @ X55 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pp]) ).
thf(c_0_11,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X51: reg] :
( ! [X52: reg] :
( ( c @ X52 @ X51 )
=> ( c @ X52 @ Z0 ) )
& ! [X53: reg] :
( ( c @ X53 @ X51 )
=> ( c @ X53 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ec]) ).
thf(c_0_12,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X49: reg] :
( ( c @ X49 @ X25 )
=> ( c @ X49 @ Z0 ) )
& ! [X50: reg] :
( ( c @ X50 @ X25 )
=> ( c @ X50 @ Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X64: reg] :
( ( c @ X64 @ Z0 )
=> ( c @ X64 @ Z1 ) )
& ~ ! [X65: reg] :
( ( c @ X65 @ Z1 )
=> ( c @ X65 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X66: reg] :
( ! [X67: reg] :
( ( c @ X67 @ X66 )
=> ( c @ X67 @ X25 ) )
& ! [X68: reg] :
( ( c @ X68 @ X66 )
=> ( c @ X68 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X69: reg] :
( ! [X70: reg] :
( ( c @ X70 @ X69 )
=> ( c @ X70 @ X25 ) )
& ! [X71: reg] :
( ( c @ X71 @ X69 )
=> ( c @ X71 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ntpp]) ).
thf(c_0_14,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X54: reg] :
( ( c @ X54 @ Z0 )
=> ( c @ X54 @ Z1 ) )
& ~ ! [X55: reg] :
( ( c @ X55 @ Z1 )
=> ( c @ X55 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_15,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X51: reg] :
( ! [X52: reg] :
( ( c @ X52 @ X51 )
=> ( c @ X52 @ Z0 ) )
& ! [X53: reg] :
( ( c @ X53 @ X51 )
=> ( c @ X53 @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ( mvalid
@ ( mbox @ fool
@ ^ [X44: $i] :
~ ? [X25: reg] :
! [X45: reg] : ( ntpp @ X25 @ X45 ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_17,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X64: reg] :
( ( c @ X64 @ Z0 )
=> ( c @ X64 @ Z1 ) )
& ~ ! [X65: reg] :
( ( c @ X65 @ Z1 )
=> ( c @ X65 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X66: reg] :
( ! [X67: reg] :
( ( c @ X67 @ X66 )
=> ( c @ X67 @ X25 ) )
& ! [X68: reg] :
( ( c @ X68 @ X66 )
=> ( c @ X68 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X69: reg] :
( ! [X70: reg] :
( ( c @ X70 @ X69 )
=> ( c @ X70 @ X25 ) )
& ! [X71: reg] :
( ( c @ X71 @ X69 )
=> ( c @ X71 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_18,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,negated_conjecture,
~ ! [X82: $i,X81: $i] :
( ~ ( fool @ X82 @ X81 )
| ~ ? [X25: reg] :
! [X45: reg] :
( ! [X72: reg] :
( ( c @ X72 @ X25 )
=> ( c @ X72 @ X45 ) )
& ~ ! [X73: reg] :
( ( c @ X73 @ X45 )
=> ( c @ X73 @ X25 ) )
& ~ ? [X74: reg] :
( ( c @ X74 @ X25 )
& ~ ? [X75: reg] :
( ! [X76: reg] :
( ( c @ X76 @ X75 )
=> ( c @ X76 @ X74 ) )
& ! [X77: reg] :
( ( c @ X77 @ X75 )
=> ( c @ X77 @ X25 ) ) )
& ( c @ X74 @ X45 )
& ~ ? [X78: reg] :
( ! [X79: reg] :
( ( c @ X79 @ X78 )
=> ( c @ X79 @ X74 ) )
& ! [X80: reg] :
( ( c @ X80 @ X78 )
=> ( c @ X80 @ X45 ) ) ) ) ) ),
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_16]),c_0_17]),c_0_18]),c_0_19])]) ).
thf(c_0_21,negated_conjecture,
! [X94: reg,X95: reg,X97: reg,X99: reg,X100: reg,X102: reg,X103: reg] :
( ( fool @ esk1_0 @ esk2_0 )
& ( ~ ( c @ X95 @ esk3_0 )
| ( c @ X95 @ X94 ) )
& ( c @ ( esk4_1 @ X94 ) @ X94 )
& ~ ( c @ ( esk4_1 @ X94 ) @ esk3_0 )
& ( ~ ( c @ X102 @ ( esk6_2 @ X94 @ X97 ) )
| ( c @ X102 @ X97 )
| ~ ( c @ X97 @ X94 )
| ~ ( c @ X99 @ ( esk5_2 @ X94 @ X97 ) )
| ( c @ X99 @ X97 )
| ~ ( c @ X97 @ esk3_0 ) )
& ( ~ ( c @ X103 @ ( esk6_2 @ X94 @ X97 ) )
| ( c @ X103 @ X94 )
| ~ ( c @ X97 @ X94 )
| ~ ( c @ X99 @ ( esk5_2 @ X94 @ X97 ) )
| ( c @ X99 @ X97 )
| ~ ( c @ X97 @ esk3_0 ) )
& ( ~ ( c @ X102 @ ( esk6_2 @ X94 @ X97 ) )
| ( c @ X102 @ X97 )
| ~ ( c @ X97 @ X94 )
| ~ ( c @ X100 @ ( esk5_2 @ X94 @ X97 ) )
| ( c @ X100 @ esk3_0 )
| ~ ( c @ X97 @ esk3_0 ) )
& ( ~ ( c @ X103 @ ( esk6_2 @ X94 @ X97 ) )
| ( c @ X103 @ X94 )
| ~ ( c @ X97 @ X94 )
| ~ ( c @ X100 @ ( esk5_2 @ X94 @ X97 ) )
| ( c @ X100 @ esk3_0 )
| ~ ( c @ X97 @ esk3_0 ) ) ),
inference(distribute,[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_22,negated_conjecture,
! [X18: reg] :
~ ( c @ ( esk4_1 @ X18 ) @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_23,negated_conjecture,
! [X18: reg] : ( c @ ( esk4_1 @ X18 ) @ X18 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_22,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG018^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n020.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Sep 29 18:35:19 UTC 2026
% 0.07/0.16 % CPUTime :
% 0.07/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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.8kCUMheGqD/E---3.1_1432889.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 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 new_ho_12 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % new_bool_2 with pid 1432905 completed with status 0
% 0.07/0.25 % Result found by new_bool_2
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 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 new_ho_12 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.25 % Search class: HGUNS-FFSF21-SHSSMSBN
% 0.07/0.25 % partial match(3): HGHNF-FFMF21-SHSSMSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 1432906 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSMSSMSSMLLNHSN.
% 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 new_ho_12 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.07/0.25 % Search class: HGUNS-FFSF21-SHSSMSBN
% 0.07/0.25 % partial match(3): HGHNF-FFMF21-SHSSMSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 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 : 98
% 0.07/0.25 % Removed by relevancy pruning/SinE : 81
% 0.07/0.25 % Initial clauses : 14
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 14
% 0.07/0.25 % Processed clauses : 4
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 4
% 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 : 1
% 0.07/0.25 % ...of the previous two non-redundant : 0
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 1
% 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 : 0
% 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 : 4
% 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 : 0
% 0.07/0.25 % Current number of unprocessed clauses: 10
% 0.07/0.25 % ...number of literals in the above : 40
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 0
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 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 : 0
% 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 : 2433
% 0.07/0.25 % Search garbage collected termcells : 1003
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.003 s
% 0.07/0.25 % System time : 0.004 s
% 0.07/0.25 % Total time : 0.007 s
% 0.07/0.25 % Maximum resident set size: 4248 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.010 s
% 0.07/0.25 % Total time : 0.014 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------