%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM684^4 : TPTP v9.3.1. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:16:49 AM UTC 2026
% Result : Theorem 0.23s 0.35s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 35 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 245 ( 18 ~; 14 |; 4 &; 193 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 64 ( 42 ^; 22 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
is_of: $i > ( $i > $o ) > $o ).
thf(decl_24,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_26,type,
in: $i > $i > $o ).
thf(decl_78,type,
e_is: $i > $i > $i > $o ).
thf(decl_124,type,
nat: $i ).
thf(decl_125,type,
n_is: $i > $i > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_154,type,
esk1_0: $i ).
thf(decl_155,type,
esk2_0: $i ).
thf(decl_156,type,
esk3_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',def_e_is) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X3: $i > $o,X2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ X3 )
=> ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',def_is_of) ).
thf(satz20e,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X303: $i] : ( in @ X303 @ nat )
@ ^ [X304: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X304 ) )
=> ( n_is @ X1 @ X304 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',satz20e) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',def_n_is) ).
thf(satz6,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X197: $i] : ( in @ X197 @ nat )
@ ^ [X198: $i] : ( n_is @ ( n_pl @ X1 @ X198 ) @ ( n_pl @ X198 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',satz6) ).
thf(satz8a,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X205: $i] : ( in @ X205 @ nat )
@ ^ [X206: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X1 @ X206 ) @ ( n_pl @ X1 @ X4 ) )
=> ( n_is @ X206 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4kRNx6eGd3/E---3.1_3929245.p',satz8a) ).
thf(c_0_7,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_8,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_all_of]) ).
thf(c_0_9,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_10,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X303: $i] : ( in @ X303 @ nat )
@ ^ [X304: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( n_is @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X304 ) )
=> ( n_is @ X1 @ X304 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz20e]) ).
thf(c_0_11,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_7]) ).
thf(c_0_12,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,negated_conjecture,
~ ! [X392: $i] :
( ( in @ X392 @ nat )
=> ! [X391: $i] :
( ( in @ X391 @ nat )
=> ! [X390: $i] :
( ( in @ X390 @ nat )
=> ( ( ( n_pl @ X390 @ X392 )
= ( n_pl @ X390 @ X391 ) )
=> ( X392 = X391 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10]),c_0_11]),c_0_12]) ).
thf(c_0_14,plain,
! [X397: $i] :
( ( in @ X397 @ nat )
=> ! [X396: $i] :
( ( in @ X396 @ nat )
=> ( ( n_pl @ X397 @ X396 )
= ( n_pl @ X396 @ X397 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_11]),c_0_12]) ).
thf(c_0_15,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk3_0 @ esk2_0 ) )
& ( esk1_0 != esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
thf(c_0_16,plain,
! [X476: $i,X477: $i] :
( ~ ( in @ X476 @ nat )
| ~ ( in @ X477 @ nat )
| ( ( n_pl @ X476 @ X477 )
= ( n_pl @ X477 @ X476 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_17,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X1: $i,X4: $i] :
( ( ( n_pl @ X1 @ X4 )
= ( n_pl @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_19,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,plain,
! [X400: $i] :
( ( in @ X400 @ nat )
=> ! [X399: $i] :
( ( in @ X399 @ nat )
=> ! [X398: $i] :
( ( in @ X398 @ nat )
=> ( ( ( n_pl @ X400 @ X399 )
= ( n_pl @ X400 @ X398 ) )
=> ( X399 = X398 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8a]),c_0_11]),c_0_12]) ).
thf(c_0_22,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk2_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
thf(c_0_23,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_24,plain,
! [X478: $i,X479: $i,X480: $i] :
( ~ ( in @ X478 @ nat )
| ~ ( in @ X479 @ nat )
| ~ ( in @ X480 @ nat )
| ( ( n_pl @ X478 @ X479 )
!= ( n_pl @ X478 @ X480 ) )
| ( X479 = X480 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
thf(c_0_25,negated_conjecture,
( ( n_pl @ esk3_0 @ esk2_0 )
= ( n_pl @ esk2_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_17,c_0_22]) ).
thf(c_0_26,negated_conjecture,
( ( n_pl @ esk2_0 @ esk3_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_23]),c_0_19])]) ).
thf(c_0_27,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ( ( n_pl @ X1 @ X4 )
!= ( n_pl @ X1 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_28,negated_conjecture,
( ( n_pl @ esk3_0 @ esk2_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ( ( n_pl @ esk3_0 @ X1 )
!= ( n_pl @ esk1_0 @ esk3_0 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_19])]) ).
thf(c_0_30,negated_conjecture,
( ( n_pl @ esk3_0 @ esk1_0 )
= ( n_pl @ esk1_0 @ esk3_0 ) ),
inference(rw,[status(thm)],[c_0_22,c_0_26]) ).
thf(c_0_31,negated_conjecture,
esk1_0 != esk2_0,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_23])]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM684^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n009.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 12:38:00 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.27 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.4kRNx6eGd3/E---3.1_3929245.p
% 0.23/0.35 % Version: 3.5.1-ho
% 0.23/0.35 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.23/0.35 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting lpo1_fix with 900s (3) cores
% 0.23/0.35 % Starting full_lambda_9 with 300s (1) cores
% 0.23/0.35 % Starting almost_fo_4 with 300s (1) cores
% 0.23/0.35 % Starting new_ho_9 with 300s (1) cores
% 0.23/0.35 % Starting pre_casc_4 with 300s (1) cores
% 0.23/0.35 % Starting ho_unfolding_6 with 300s (1) cores
% 0.23/0.35 % pre_casc_4 with pid 3929282 completed with status 0
% 0.23/0.35 % Result found by pre_casc_4
% 0.23/0.35 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.23/0.35 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting lpo1_fix with 900s (3) cores
% 0.23/0.35 % Starting full_lambda_9 with 300s (1) cores
% 0.23/0.35 % Starting almost_fo_4 with 300s (1) cores
% 0.23/0.35 % Starting new_ho_9 with 300s (1) cores
% 0.23/0.35 % Starting pre_casc_4 with 300s (1) cores
% 0.23/0.35 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.23/0.35 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.23/0.35 % Search class: HGUSM-FFMM31-DHSMMSBN
% 0.23/0.35 % partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.23/0.35 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.35 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.35 % SubtermCWHack with pid 3929284 completed with status 0
% 0.23/0.35 % Result found by SubtermCWHack
% 0.23/0.35 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.23/0.35 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.35 % Starting lpo1_fix with 900s (3) cores
% 0.23/0.35 % Starting full_lambda_9 with 300s (1) cores
% 0.23/0.35 % Starting almost_fo_4 with 300s (1) cores
% 0.23/0.35 % Starting new_ho_9 with 300s (1) cores
% 0.23/0.35 % Starting pre_casc_4 with 300s (1) cores
% 0.23/0.35 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.23/0.35 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.23/0.35 % Search class: HGUSM-FFMM31-DHSMMSBN
% 0.23/0.35 % partial match(3): HGHSM-FFMM31-SHSSMSBN
% 0.23/0.35 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.35 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.35 % Preprocessing time : 0.004 s
% 0.23/0.35
% 0.23/0.35 % Proof found!
% 0.23/0.35 % SZS status Theorem
% 0.23/0.35 % SZS output start CNFRefutation
% See solution above
% 0.23/0.35 % Parsed axioms : 387
% 0.23/0.35 % Removed by relevancy pruning/SinE : 314
% 0.23/0.35 % Initial clauses : 113
% 0.23/0.35 % Removed in clause preprocessing : 5
% 0.23/0.35 % Initial clauses in saturation : 108
% 0.23/0.35 % Processed clauses : 393
% 0.23/0.35 % ...of these trivial : 33
% 0.23/0.35 % ...subsumed : 135
% 0.23/0.35 % ...remaining for further processing : 225
% 0.23/0.35 % Other redundant clauses eliminated : 17
% 0.23/0.35 % Clauses deleted for lack of memory : 0
% 0.23/0.35 % Backward-subsumed : 1
% 0.23/0.35 % Backward-rewritten : 10
% 0.23/0.35 % Generated clauses : 954
% 0.23/0.35 % ...of the previous two non-redundant : 868
% 0.23/0.35 % ...aggressively subsumed : 0
% 0.23/0.35 % Contextual simplify-reflections : 1
% 0.23/0.35 % Paramodulations : 928
% 0.23/0.35 % Factorizations : 2
% 0.23/0.35 % NegExts : 0
% 0.23/0.35 % Equation resolutions : 20
% 0.23/0.35 % Disequality decompositions : 0
% 0.23/0.35 % Total rewrite steps : 204
% 0.23/0.35 % ...of those cached : 146
% 0.23/0.35 % Propositional unsat checks : 0
% 0.23/0.35 % Propositional check models : 0
% 0.23/0.35 % Propositional check unsatisfiable : 0
% 0.23/0.35 % Propositional clauses : 0
% 0.23/0.35 % Propositional clauses after purity: 0
% 0.23/0.35 % Propositional unsat core size : 0
% 0.23/0.35 % Propositional preprocessing time : 0.000
% 0.23/0.35 % Propositional encoding time : 0.000
% 0.23/0.35 % Propositional solver time : 0.000
% 0.23/0.35 % Success case prop preproc time : 0.000
% 0.23/0.35 % Success case prop encoding time : 0.000
% 0.23/0.35 % Success case prop solver time : 0.000
% 0.23/0.35 % Current number of processed clauses : 213
% 0.23/0.35 % Positive orientable unit clauses : 56
% 0.23/0.35 % Positive unorientable unit clauses: 0
% 0.23/0.35 % Negative unit clauses : 29
% 0.23/0.35 % Non-unit-clauses : 128
% 0.23/0.35 % Current number of unprocessed clauses: 575
% 0.23/0.35 % ...number of literals in the above : 1704
% 0.23/0.35 % Current number of archived formulas : 0
% 0.23/0.35 % Current number of archived clauses : 11
% 0.23/0.35 % Clause-clause subsumption calls (NU) : 1669
% 0.23/0.35 % Rec. Clause-clause subsumption calls : 1120
% 0.23/0.35 % Non-unit clause-clause subsumptions : 49
% 0.23/0.35 % Unit Clause-clause subsumption calls : 96
% 0.23/0.35 % Rewrite failures with RHS unbound : 0
% 0.23/0.35 % BW rewrite match attempts : 92
% 0.23/0.35 % BW rewrite match successes : 9
% 0.23/0.35 % Condensation attempts : 0
% 0.23/0.35 % Condensation successes : 0
% 0.23/0.35 % Termbank termtop insertions : 32529
% 0.23/0.35 % Search garbage collected termcells : 6419
% 0.23/0.35
% 0.23/0.35 % -------------------------------------------------
% 0.23/0.35 % User time : 0.055 s
% 0.23/0.35 % System time : 0.006 s
% 0.23/0.35 % Total time : 0.061 s
% 0.23/0.35 % Maximum resident set size: 5032 pages
% 0.23/0.35
% 0.23/0.35 % -------------------------------------------------
% 0.23/0.35 % User time : 0.061 s
% 0.23/0.35 % System time : 0.010 s
% 0.23/0.35 % Total time : 0.071 s
% 0.23/0.35 % Maximum resident set size: 5376 pages
% 0.23/0.35 % E exiting
%------------------------------------------------------------------------------