%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : CSR150^1 : 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 : 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 07:46:41 AM UTC 2026
% Result : Theorem 0.24s 0.28s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 1 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 229 ( 30 ~; 24 |; 6 &; 166 @)
% ( 2 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 8 ^; 40 !; 5 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
grandchild_THFTYPE_IiioI: $i > $i > $o ).
thf(decl_24,type,
grandparent_THFTYPE_IiioI: $i > $i > $o ).
thf(decl_25,type,
lCardinalityFn_THFTYPE_IIioIiI: ( $i > $o ) > $i ).
thf(decl_26,type,
lJohn_THFTYPE_i: $i ).
thf(decl_27,type,
ltet_THFTYPE_IiioI: $i > $i > $o ).
thf(decl_28,type,
n3_THFTYPE_i: $i ).
thf(decl_29,type,
parent_THFTYPE_IiioI: $i > $i > $o ).
thf(decl_30,type,
esk1_2: $i > $i > $i ).
thf(decl_31,type,
esk2_2: $i > $i > $i ).
thf(decl_32,type,
esk1_0: $i ).
thf(con,conjecture,
? [X2: $i] :
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ X2 ),
file('/export/starexec/sandbox2/tmp/tmp.8YOa57NiEZ/E---3.1_430413.p',con) ).
thf(ax_001,axiom,
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ X1 ) )
@ n3_THFTYPE_i ),
file('/export/starexec/sandbox2/tmp/tmp.8YOa57NiEZ/E---3.1_430413.p',ax_001) ).
thf(ax,axiom,
! [X1: $i,X2: $i] :
( ( grandparent_THFTYPE_IiioI @ X1 @ X2 )
<=> ? [X3: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ X3 )
& ( parent_THFTYPE_IiioI @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8YOa57NiEZ/E---3.1_430413.p',ax) ).
thf(ax_002,axiom,
! [X1: $i,X2: $i] :
( ( grandchild_THFTYPE_IiioI @ X1 @ X2 )
<=> ? [X3: $i] :
( ( parent_THFTYPE_IiioI @ X3 @ X1 )
& ( parent_THFTYPE_IiioI @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.8YOa57NiEZ/E---3.1_430413.p',ax_002) ).
thf(c_0_4,negated_conjecture,
~ ? [X2: $i] :
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [X1: $i] : ( grandchild_THFTYPE_IiioI @ X1 @ lJohn_THFTYPE_i ) )
@ X2 ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_5,negated_conjecture,
~ ? [X2: $i] :
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Z0: $i] : ( grandchild_THFTYPE_IiioI @ Z0 @ lJohn_THFTYPE_i ) )
@ X2 ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X23: $i] :
~ ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Z0: $i] : ( grandchild_THFTYPE_IiioI @ Z0 @ lJohn_THFTYPE_i ) )
@ X23 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_7,plain,
( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Z0: $i] : ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ Z0 ) )
@ n3_THFTYPE_i ),
inference(fof_simplification,[status(thm)],[ax_001]) ).
thf(c_0_8,plain,
! [X11: $i,X12: $i,X14: $i,X15: $i,X16: $i] :
( ( ( parent_THFTYPE_IiioI @ X11 @ ( esk1_2 @ X11 @ X12 ) )
| ~ ( grandparent_THFTYPE_IiioI @ X11 @ X12 ) )
& ( ( parent_THFTYPE_IiioI @ ( esk1_2 @ X11 @ X12 ) @ X12 )
| ~ ( grandparent_THFTYPE_IiioI @ X11 @ X12 ) )
& ( ~ ( parent_THFTYPE_IiioI @ X14 @ X16 )
| ~ ( parent_THFTYPE_IiioI @ X16 @ X15 )
| ( grandparent_THFTYPE_IiioI @ X14 @ X15 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ax])])])])])])]) ).
thf(c_0_9,plain,
! [X17: $i,X18: $i,X20: $i,X21: $i,X22: $i] :
( ( ( parent_THFTYPE_IiioI @ ( esk2_2 @ X17 @ X18 ) @ X17 )
| ~ ( grandchild_THFTYPE_IiioI @ X17 @ X18 ) )
& ( ( parent_THFTYPE_IiioI @ X18 @ ( esk2_2 @ X17 @ X18 ) )
| ~ ( grandchild_THFTYPE_IiioI @ X17 @ X18 ) )
& ( ~ ( parent_THFTYPE_IiioI @ X22 @ X20 )
| ~ ( parent_THFTYPE_IiioI @ X21 @ X22 )
| ( grandchild_THFTYPE_IiioI @ X20 @ X21 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_002])])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
~ ( ltet_THFTYPE_IiioI
@ ( lCardinalityFn_THFTYPE_IIioIiI
@ ^ [Z0: $i] : ( grandchild_THFTYPE_IiioI @ Z0 @ lJohn_THFTYPE_i ) )
@ X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
ltet_THFTYPE_IiioI @ ( lCardinalityFn_THFTYPE_IIioIiI @ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i ) ) @ n3_THFTYPE_i,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( grandparent_THFTYPE_IiioI @ X1 @ X3 )
| ~ ( parent_THFTYPE_IiioI @ X1 @ X2 )
| ~ ( parent_THFTYPE_IiioI @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X1: $i,X2: $i] :
( ( parent_THFTYPE_IiioI @ ( esk2_2 @ X1 @ X2 ) @ X1 )
| ~ ( grandchild_THFTYPE_IiioI @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
( ( ^ [Z0: $i] : ( grandchild_THFTYPE_IiioI @ Z0 @ lJohn_THFTYPE_i ) )
!= ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i ) ),
inference(er,[status(thm)],[inference(ext_sup,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_15,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( grandparent_THFTYPE_IiioI @ X1 @ X2 )
| ~ ( parent_THFTYPE_IiioI @ X1 @ ( esk2_2 @ X2 @ X3 ) )
| ~ ( grandchild_THFTYPE_IiioI @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,plain,
! [X2: $i,X1: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ ( esk2_2 @ X2 @ X1 ) )
| ~ ( grandchild_THFTYPE_IiioI @ X2 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,plain,
( ( grandchild_THFTYPE_IiioI @ esk1_0 @ lJohn_THFTYPE_i )
<~> ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ esk1_0 ) ),
inference(neg_ext,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
! [X2: $i,X1: $i] :
( ( grandparent_THFTYPE_IiioI @ X1 @ X2 )
| ~ ( grandchild_THFTYPE_IiioI @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,plain,
( ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ esk1_0 )
| ( grandchild_THFTYPE_IiioI @ esk1_0 @ lJohn_THFTYPE_i ) ),
inference(dynamic_cnf,[status(thm)],[c_0_17]) ).
thf(c_0_20,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( grandchild_THFTYPE_IiioI @ X2 @ X3 )
| ~ ( parent_THFTYPE_IiioI @ X1 @ X2 )
| ~ ( parent_THFTYPE_IiioI @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_21,plain,
! [X1: $i,X2: $i] :
( ( parent_THFTYPE_IiioI @ X1 @ ( esk1_2 @ X1 @ X2 ) )
| ~ ( grandparent_THFTYPE_IiioI @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_22,plain,
( ~ ( grandchild_THFTYPE_IiioI @ esk1_0 @ lJohn_THFTYPE_i )
| ~ ( grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ esk1_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
grandparent_THFTYPE_IiioI @ lJohn_THFTYPE_i @ esk1_0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( grandchild_THFTYPE_IiioI @ X1 @ X2 )
| ~ ( parent_THFTYPE_IiioI @ ( esk1_2 @ X2 @ X3 ) @ X1 )
| ~ ( grandparent_THFTYPE_IiioI @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_25,plain,
! [X1: $i,X2: $i] :
( ( parent_THFTYPE_IiioI @ ( esk1_2 @ X1 @ X2 ) @ X2 )
| ~ ( grandparent_THFTYPE_IiioI @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_26,plain,
~ ( grandchild_THFTYPE_IiioI @ esk1_0 @ lJohn_THFTYPE_i ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
thf(c_0_27,plain,
! [X2: $i,X1: $i] :
( ( grandchild_THFTYPE_IiioI @ X1 @ X2 )
| ~ ( grandparent_THFTYPE_IiioI @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_28,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CSR150^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:59:56 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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.8YOa57NiEZ/E---3.1_430413.p
% 0.24/0.28 % Version: 3.5.1-ho
% 0.24/0.28 % Preprocessing class: HSSSSMSSSSMCSSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting post_as_ho5 with 1500s (5) cores
% 0.24/0.28 % Starting sh5l with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho10 with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho4 with 300s (1) cores
% 0.24/0.28 % post_as_ho10 with pid 430428 completed with status 0
% 0.24/0.28 % Result found by post_as_ho10
% 0.24/0.28 % Preprocessing class: HSSSSMSSSSMCSSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting post_as_ho5 with 1500s (5) cores
% 0.24/0.28 % Starting sh5l with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho10 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.28 % No SInE strategy applied
% 0.24/0.28 % Search class: HHUNF-FFSF21-MSSFFFNN
% 0.24/0.28 % partial match(2): HHUNF-FFSF22-SSSFFFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % SubtermCWHack with pid 430434 completed with status 10
% 0.24/0.28 % Starting post_as_ho10 with 31s (1) cores
% 0.24/0.28 % post_as_ho10 with pid 430440 completed with status 0
% 0.24/0.28 % Result found by post_as_ho10
% 0.24/0.28 % Preprocessing class: HSSSSMSSSSMCSSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting post_as_ho5 with 1500s (5) cores
% 0.24/0.28 % Starting sh5l with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho10 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.28 % No SInE strategy applied
% 0.24/0.28 % Search class: HHUNF-FFSF21-MSSFFFNN
% 0.24/0.28 % partial match(2): HHUNF-FFSF22-SSSFFFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % SubtermCWHack with pid 430434 completed with status 10
% 0.24/0.28 % Starting post_as_ho10 with 31s (1) cores
% 0.24/0.28 % Preprocessing time : 0.001 s
% 0.24/0.28 % Presaturation interreduction done
% 0.24/0.28
% 0.24/0.28 % Proof found!
% 0.24/0.28 % SZS status Theorem
% 0.24/0.28 % SZS output start CNFRefutation
% See solution above
% 0.24/0.28 % Parsed axioms : 12
% 0.24/0.28 % Removed by relevancy pruning/SinE : 0
% 0.24/0.28 % Initial clauses : 16
% 0.24/0.28 % Removed in clause preprocessing : 8
% 0.24/0.28 % Initial clauses in saturation : 8
% 0.24/0.28 % Processed clauses : 27
% 0.24/0.28 % ...of these trivial : 0
% 0.24/0.28 % ...subsumed : 0
% 0.24/0.28 % ...remaining for further processing : 27
% 0.24/0.28 % Other redundant clauses eliminated : 1
% 0.24/0.28 % Clauses deleted for lack of memory : 0
% 0.24/0.28 % Backward-subsumed : 0
% 0.24/0.28 % Backward-rewritten : 2
% 0.24/0.28 % Generated clauses : 26
% 0.24/0.28 % ...of the previous two non-redundant : 22
% 0.24/0.28 % ...aggressively subsumed : 0
% 0.24/0.28 % Contextual simplify-reflections : 0
% 0.24/0.28 % Paramodulations : 21
% 0.24/0.28 % Factorizations : 0
% 0.24/0.28 % NegExts : 1
% 0.24/0.28 % Equation resolutions : 1
% 0.24/0.28 % Disequality decompositions : 0
% 0.24/0.28 % Total rewrite steps : 3
% 0.24/0.28 % ...of those cached : 2
% 0.24/0.28 % Propositional unsat checks : 0
% 0.24/0.28 % Propositional check models : 0
% 0.24/0.28 % Propositional check unsatisfiable : 0
% 0.24/0.28 % Propositional clauses : 0
% 0.24/0.28 % Propositional clauses after purity: 0
% 0.24/0.28 % Propositional unsat core size : 0
% 0.24/0.28 % Propositional preprocessing time : 0.000
% 0.24/0.28 % Propositional encoding time : 0.000
% 0.24/0.28 % Propositional solver time : 0.000
% 0.24/0.28 % Success case prop preproc time : 0.000
% 0.24/0.28 % Success case prop encoding time : 0.000
% 0.24/0.28 % Success case prop solver time : 0.000
% 0.24/0.28 % Current number of processed clauses : 16
% 0.24/0.28 % Positive orientable unit clauses : 2
% 0.24/0.28 % Positive unorientable unit clauses: 0
% 0.24/0.28 % Negative unit clauses : 3
% 0.24/0.28 % Non-unit-clauses : 11
% 0.24/0.28 % Current number of unprocessed clauses: 11
% 0.24/0.28 % ...number of literals in the above : 33
% 0.24/0.28 % Current number of archived formulas : 0
% 0.24/0.28 % Current number of archived clauses : 11
% 0.24/0.28 % Clause-clause subsumption calls (NU) : 18
% 0.24/0.28 % Rec. Clause-clause subsumption calls : 16
% 0.24/0.28 % Non-unit clause-clause subsumptions : 0
% 0.24/0.28 % Unit Clause-clause subsumption calls : 6
% 0.24/0.28 % Rewrite failures with RHS unbound : 0
% 0.24/0.28 % BW rewrite match attempts : 1
% 0.24/0.28 % BW rewrite match successes : 1
% 0.24/0.28 % Condensation attempts : 0
% 0.24/0.28 % Condensation successes : 0
% 0.24/0.28 % Termbank termtop insertions : 1478
% 0.24/0.28 % Search garbage collected termcells : 180
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.011 s
% 0.24/0.28 % System time : 0.001 s
% 0.24/0.28 % Total time : 0.012 s
% 0.24/0.28 % Maximum resident set size: 3632 pages
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.015 s
% 0.24/0.28 % System time : 0.004 s
% 0.24/0.28 % Total time : 0.019 s
% 0.24/0.28 % Maximum resident set size: 4864 pages
% 0.24/0.28 % E exiting
%------------------------------------------------------------------------------