%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM668^4 : 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 : n001.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 08:17:22 AM UTC 2026
% Result : Theorem 0.45s 0.37s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 40 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 180 ( 29 ~; 5 |; 3 &; 111 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 83 ( 68 ^; 15 !; 0 ?; 83 :)
% 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_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $o > $o ).
thf(decl_72,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(decl_73,type,
l_some: $i > ( $i > $o ) > $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_128,type,
n_some: ( $i > $o ) > $o ).
thf(decl_143,type,
n_pl: $i > $i > $i ).
thf(decl_148,type,
diffprop: $i > $i > $i > $o ).
thf(decl_149,type,
d_29_ii: $i > $i > $o ).
thf(decl_217,type,
esk60_0: $i ).
thf(decl_218,type,
esk61_0: $i ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_imp) ).
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.5UMjSh2Thq/E---3.1_1178337.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_is_of) ).
thf(def_non,axiom,
( non
= ( ^ [X1: $i,X2: $i > $o,X4: $i] : ( d_not @ ( X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_non) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X1: $i,X2: $i > $o] :
( d_not
@ ( all_of
@ ^ [X4: $i] : ( in @ X4 @ X1 )
@ ( non @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_l_some) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_e_is) ).
thf(def_diffprop,axiom,
( diffprop
= ( ^ [X1: $i,X207: $i,X4: $i] : ( n_is @ X1 @ ( n_pl @ X207 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_diffprop) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_n_is) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_d_29_ii) ).
thf(def_n_some,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X437: $i] :
( ( in @ X437 @ nat )
=> ( ( Z0 @ X437 )
=> ~ $true ) )
=> ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',def_n_some) ).
thf(satz18,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X263: $i] : ( in @ X263 @ nat )
@ ^ [X264: $i] : ( d_29_ii @ ( n_pl @ X1 @ X264 ) @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5UMjSh2Thq/E---3.1_1178337.p',satz18) ).
thf(c_0_12,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_13,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_14,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_15,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_16,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_non]) ).
thf(c_0_17,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X410: $i] :
( ( in @ X410 @ Z0 )
=> ( ( Z1 @ X410 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_l_some]) ).
thf(c_0_19,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,plain,
( non
= ( ^ [Z0: $i,Z1: $i > $o,Z2: $i] :
( ( Z1 @ Z2 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_22,plain,
( l_some
= ( ^ [Z0: $i,Z1: $i > $o] :
( ! [X410: $i] :
( ( in @ X410 @ Z0 )
=> ( ( Z1 @ X410 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_18,c_0_19]),c_0_17]),c_0_20]) ).
thf(c_0_23,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_diffprop]) ).
thf(c_0_24,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_21]) ).
thf(c_0_25,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X448: $i] :
( ( in @ X448 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X448 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_26,axiom,
( n_some
= ( ^ [Z0: $i > $o] :
( ! [X437: $i] :
( ( in @ X437 @ nat )
=> ( ( Z0 @ X437 )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[def_n_some,c_0_22]) ).
thf(c_0_27,plain,
( diffprop
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( Z0
= ( n_pl @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_28,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X263: $i] : ( in @ X263 @ nat )
@ ^ [X264: $i] : ( d_29_ii @ ( n_pl @ X1 @ X264 ) @ X1 ) ) ),
inference(assume_negation,[status(cth)],[satz18]) ).
thf(c_0_29,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] :
( ! [X448: $i] :
( ( in @ X448 @ nat )
=> ( ( Z0
= ( n_pl @ Z1 @ X448 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_30,negated_conjecture,
~ ! [X688: $i] :
( ( in @ X688 @ nat )
=> ! [X687: $i] :
( ( in @ X687 @ nat )
=> ( ! [X686: $i] :
( ( in @ X686 @ nat )
=> ( ( ( n_pl @ X688 @ X687 )
= ( n_pl @ X688 @ X686 ) )
=> ~ $true ) )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_28]),c_0_19]),c_0_29]) ).
thf(c_0_31,negated_conjecture,
! [X1305: $i] :
( ( in @ esk60_0 @ nat )
& ( in @ esk61_0 @ nat )
& ( ~ ( in @ X1305 @ nat )
| ( ( n_pl @ esk60_0 @ esk61_0 )
!= ( n_pl @ esk60_0 @ X1305 ) )
| ~ $true )
& $true ),
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_30])])])])]) ).
thf(c_0_32,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ nat )
| ( ( n_pl @ esk60_0 @ esk61_0 )
!= ( n_pl @ esk60_0 @ X1 ) )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_33,negated_conjecture,
! [X1: $i] :
( ( ( n_pl @ esk60_0 @ esk61_0 )
!= ( n_pl @ esk60_0 @ X1 ) )
| ~ ( in @ X1 @ nat ) ),
inference(cn,[status(thm)],[c_0_32]) ).
thf(c_0_34,negated_conjecture,
in @ esk61_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM668^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:40:20 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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.5UMjSh2Thq/E---3.1_1178337.p
% 0.45/0.37 % Version: 3.5.1-ho
% 0.45/0.37 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.45/0.37 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.37 % Starting lpo1_fix with 900s (3) cores
% 0.45/0.37 % Starting full_lambda_9 with 300s (1) cores
% 0.45/0.37 % Starting almost_fo_4 with 300s (1) cores
% 0.45/0.37 % Starting new_ho_9 with 300s (1) cores
% 0.45/0.37 % Starting pre_casc_4 with 300s (1) cores
% 0.45/0.37 % Starting ho_unfolding_6 with 300s (1) cores
% 0.45/0.37 % almost_fo_4 with pid 1178352 completed with status 0
% 0.45/0.37 % Result found by almost_fo_4
% 0.45/0.37 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.45/0.37 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.37 % Starting lpo1_fix with 900s (3) cores
% 0.45/0.37 % Starting full_lambda_9 with 300s (1) cores
% 0.45/0.37 % Starting almost_fo_4 with 300s (1) cores
% 0.45/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.45/0.37 % No SInE strategy applied
% 0.45/0.37 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.45/0.37 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.45/0.37 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.45/0.37 % Starting SubtermCWHack with 31s (1) cores
% 0.45/0.37 % SubtermCWHack with pid 1178359 completed with status 0
% 0.45/0.37 % Result found by SubtermCWHack
% 0.45/0.37 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.45/0.37 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.37 % Starting lpo1_fix with 900s (3) cores
% 0.45/0.37 % Starting full_lambda_9 with 300s (1) cores
% 0.45/0.37 % Starting almost_fo_4 with 300s (1) cores
% 0.45/0.37 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.45/0.37 % No SInE strategy applied
% 0.45/0.37 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.45/0.37 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.45/0.37 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.45/0.37 % Starting SubtermCWHack with 31s (1) cores
% 0.45/0.37 % Preprocessing time : 0.009 s
% 0.45/0.37
% 0.45/0.37 % Proof found!
% 0.45/0.37 % SZS status Theorem
% 0.45/0.37 % SZS output start CNFRefutation
% See solution above
% 0.45/0.38 % Parsed axioms : 365
% 0.45/0.38 % Removed by relevancy pruning/SinE : 0
% 0.45/0.38 % Initial clauses : 771
% 0.45/0.38 % Removed in clause preprocessing : 467
% 0.45/0.38 % Initial clauses in saturation : 304
% 0.45/0.38 % Processed clauses : 140
% 0.45/0.38 % ...of these trivial : 12
% 0.45/0.38 % ...subsumed : 15
% 0.45/0.38 % ...remaining for further processing : 113
% 0.45/0.38 % Other redundant clauses eliminated : 11
% 0.45/0.38 % Clauses deleted for lack of memory : 0
% 0.45/0.38 % Backward-subsumed : 0
% 0.45/0.38 % Backward-rewritten : 0
% 0.45/0.38 % Generated clauses : 157
% 0.45/0.38 % ...of the previous two non-redundant : 129
% 0.45/0.38 % ...aggressively subsumed : 0
% 0.45/0.38 % Contextual simplify-reflections : 1
% 0.45/0.38 % Paramodulations : 131
% 0.45/0.38 % Factorizations : 0
% 0.45/0.38 % NegExts : 0
% 0.45/0.38 % Equation resolutions : 13
% 0.45/0.38 % Disequality decompositions : 0
% 0.45/0.38 % Total rewrite steps : 27
% 0.45/0.38 % ...of those cached : 9
% 0.45/0.38 % Propositional unsat checks : 0
% 0.45/0.38 % Propositional check models : 0
% 0.45/0.38 % Propositional check unsatisfiable : 0
% 0.45/0.38 % Propositional clauses : 0
% 0.45/0.38 % Propositional clauses after purity: 0
% 0.45/0.38 % Propositional unsat core size : 0
% 0.45/0.38 % Propositional preprocessing time : 0.000
% 0.45/0.38 % Propositional encoding time : 0.000
% 0.45/0.38 % Propositional solver time : 0.000
% 0.45/0.38 % Success case prop preproc time : 0.000
% 0.45/0.38 % Success case prop encoding time : 0.000
% 0.45/0.38 % Success case prop solver time : 0.000
% 0.45/0.38 % Current number of processed clauses : 113
% 0.45/0.38 % Positive orientable unit clauses : 51
% 0.45/0.38 % Positive unorientable unit clauses: 1
% 0.45/0.38 % Negative unit clauses : 10
% 0.45/0.38 % Non-unit-clauses : 51
% 0.45/0.38 % Current number of unprocessed clauses: 293
% 0.45/0.38 % ...number of literals in the above : 1162
% 0.45/0.38 % Current number of archived formulas : 0
% 0.45/0.38 % Current number of archived clauses : 0
% 0.45/0.38 % Clause-clause subsumption calls (NU) : 457
% 0.45/0.38 % Rec. Clause-clause subsumption calls : 374
% 0.45/0.38 % Non-unit clause-clause subsumptions : 9
% 0.45/0.38 % Unit Clause-clause subsumption calls : 432
% 0.45/0.38 % Rewrite failures with RHS unbound : 0
% 0.45/0.38 % BW rewrite match attempts : 18
% 0.45/0.38 % BW rewrite match successes : 0
% 0.45/0.38 % Condensation attempts : 0
% 0.45/0.38 % Condensation successes : 0
% 0.45/0.38 % Termbank termtop insertions : 76512
% 0.45/0.38 % Search garbage collected termcells : 27134
% 0.45/0.38
% 0.45/0.38 % -------------------------------------------------
% 0.45/0.38 % User time : 0.062 s
% 0.45/0.38 % System time : 0.019 s
% 0.45/0.38 % Total time : 0.081 s
% 0.45/0.38 % Maximum resident set size: 7780 pages
% 0.45/0.38
% 0.45/0.38 % -------------------------------------------------
% 0.45/0.38 % User time : 0.071 s
% 0.45/0.38 % System time : 0.027 s
% 0.45/0.38 % Total time : 0.098 s
% 0.45/0.38 % Maximum resident set size: 5376 pages
% 0.45/0.38 % E exiting
%------------------------------------------------------------------------------