%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM683^4 : 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 : n005.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 0.57s 0.46s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 135 ( 23 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 302 ( 16 ~; 12 |; 4 &; 254 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 75 ( 54 ^; 21 !; 0 ?; 75 :)
% 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_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_150,type,
iii: $i > $i > $o ).
thf(decl_156,type,
esk1_0: $i ).
thf(decl_157,type,
esk2_0: $i ).
thf(decl_158,type,
esk3_0: $i ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X1: $i,X210: $i] : ( n_some @ ( diffprop @ X1 @ X210 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',def_d_29_ii) ).
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.Y1Row1aPj2/E---3.1_1601444.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',def_is_of) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',def_e_is) ).
thf(satz20d,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X301: $i] : ( in @ X301 @ nat )
@ ^ [X302: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( d_29_ii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X302 ) )
=> ( d_29_ii @ X1 @ X302 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',satz20d) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',def_n_some) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',def_n_is) ).
thf(def_iii,axiom,
( iii
= ( ^ [X1: $i,X211: $i] : ( n_some @ ( diffprop @ X211 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',def_iii) ).
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.Y1Row1aPj2/E---3.1_1601444.p',satz6) ).
thf(satz20c,axiom,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X299: $i] : ( in @ X299 @ nat )
@ ^ [X300: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( iii @ ( n_pl @ X1 @ X4 ) @ ( n_pl @ X300 @ X4 ) )
=> ( iii @ X1 @ X300 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Y1Row1aPj2/E---3.1_1601444.p',satz20c) ).
thf(c_0_10,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_d_29_ii]) ).
thf(c_0_11,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_12,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_13,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_14,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X301: $i] : ( in @ X301 @ nat )
@ ^ [X302: $i] :
( all_of
@ ^ [X4: $i] : ( in @ X4 @ nat )
@ ^ [X4: $i] :
( ( d_29_ii @ ( n_pl @ X4 @ X1 ) @ ( n_pl @ X4 @ X302 ) )
=> ( d_29_ii @ X1 @ X302 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz20d]) ).
thf(c_0_15,plain,
( d_29_ii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z0 @ Z1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_10,def_n_some]) ).
thf(c_0_16,plain,
( all_of
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X4: $i] :
( ( Z0 @ X4 )
=> ( Z1 @ X4 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_13]) ).
thf(c_0_18,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[def_iii]) ).
thf(c_0_19,negated_conjecture,
~ ! [X372: $i] :
( ( in @ X372 @ nat )
=> ! [X371: $i] :
( ( in @ X371 @ nat )
=> ! [X370: $i] :
( ( in @ X370 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X370 @ X372 ) @ ( n_pl @ X370 @ X371 ) ) )
=> ( l_some @ nat @ ( diffprop @ X372 @ X371 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_20,plain,
! [X387: $i] :
( ( in @ X387 @ nat )
=> ! [X386: $i] :
( ( in @ X386 @ nat )
=> ( ( n_pl @ X387 @ X386 )
= ( n_pl @ X386 @ X387 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]),c_0_16]),c_0_17]) ).
thf(c_0_21,plain,
( iii
= ( ^ [Z0: $i,Z1: $i] : ( l_some @ nat @ ( diffprop @ Z1 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_18,def_n_some]) ).
thf(c_0_22,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( in @ esk3_0 @ nat )
& ( l_some @ nat @ ( diffprop @ ( n_pl @ esk3_0 @ esk1_0 ) @ ( n_pl @ esk3_0 @ esk2_0 ) ) )
& ~ ( l_some @ nat @ ( diffprop @ 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_19])])])]) ).
thf(c_0_23,plain,
! [X555: $i,X556: $i] :
( ~ ( in @ X555 @ nat )
| ~ ( in @ X556 @ nat )
| ( ( n_pl @ X555 @ X556 )
= ( n_pl @ X556 @ X555 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
thf(c_0_24,plain,
! [X477: $i] :
( ( in @ X477 @ nat )
=> ! [X476: $i] :
( ( in @ X476 @ nat )
=> ! [X475: $i] :
( ( in @ X475 @ nat )
=> ( ( l_some @ nat @ ( diffprop @ ( n_pl @ X476 @ X475 ) @ ( n_pl @ X477 @ X475 ) ) )
=> ( l_some @ nat @ ( diffprop @ X476 @ X477 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz20c]),c_0_21]),c_0_16]) ).
thf(c_0_25,negated_conjecture,
l_some @ nat @ ( diffprop @ ( n_pl @ esk3_0 @ esk1_0 ) @ ( n_pl @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,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_23]) ).
thf(c_0_27,negated_conjecture,
in @ esk3_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,negated_conjecture,
in @ esk2_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_29,plain,
! [X640: $i,X641: $i,X642: $i] :
( ~ ( in @ X640 @ nat )
| ~ ( in @ X641 @ nat )
| ~ ( in @ X642 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ X641 @ X642 ) @ ( n_pl @ X640 @ X642 ) ) )
| ( l_some @ nat @ ( diffprop @ X641 @ X640 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
thf(c_0_30,negated_conjecture,
l_some @ nat @ ( diffprop @ ( 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_25,c_0_26]),c_0_27]),c_0_28])]) ).
thf(c_0_31,negated_conjecture,
in @ esk1_0 @ nat,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_32,plain,
! [X1: $i,X4: $i,X5: $i] :
( ( l_some @ nat @ ( diffprop @ X4 @ X1 ) )
| ~ ( in @ X1 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X5 @ nat )
| ~ ( l_some @ nat @ ( diffprop @ ( n_pl @ X4 @ X5 ) @ ( n_pl @ X1 @ X5 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
thf(c_0_33,negated_conjecture,
l_some @ nat @ ( diffprop @ ( n_pl @ esk1_0 @ esk3_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_30,c_0_26]),c_0_31]),c_0_27])]) ).
thf(c_0_34,negated_conjecture,
~ ( l_some @ nat @ ( diffprop @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27]),c_0_31]),c_0_28])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM683^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n005.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 12:37:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.23/0.27 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.Y1Row1aPj2/E---3.1_1601444.p
% 0.57/0.46 % Version: 3.5.1-ho
% 0.57/0.46 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.57/0.46 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.46 % Starting lpo1_fix with 900s (3) cores
% 0.57/0.46 % Starting full_lambda_9 with 300s (1) cores
% 0.57/0.46 % Starting almost_fo_4 with 300s (1) cores
% 0.57/0.46 % Starting new_ho_9 with 300s (1) cores
% 0.57/0.46 % Starting pre_casc_4 with 300s (1) cores
% 0.57/0.46 % Starting ho_unfolding_6 with 300s (1) cores
% 0.57/0.46 % full_lambda_9 with pid 1601458 completed with status 0
% 0.57/0.46 % Result found by full_lambda_9
% 0.57/0.46 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.57/0.46 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.46 % Starting lpo1_fix with 900s (3) cores
% 0.57/0.46 % Starting full_lambda_9 with 300s (1) cores
% 0.57/0.46 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.57/0.46 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.57/0.46 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.57/0.46 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.57/0.46 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.57/0.46 % SubtermCWHack with pid 1601463 completed with status 0
% 0.57/0.46 % Result found by SubtermCWHack
% 0.57/0.46 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.57/0.46 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.46 % Starting lpo1_fix with 900s (3) cores
% 0.57/0.46 % Starting full_lambda_9 with 300s (1) cores
% 0.57/0.46 % (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
% 0.57/0.46 % SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
% 0.57/0.46 % Search class: HGHSM-FSLM32-DHSMMSBN
% 0.57/0.46 % partial match(1): HGHSM-FSLM32-MHSMMSBN
% 0.57/0.46 % Scheduled 12 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.57/0.46 % Preprocessing time : 0.006 s
% 0.57/0.46
% 0.57/0.46 % Proof found!
% 0.57/0.46 % SZS status Theorem
% 0.57/0.46 % SZS output start CNFRefutation
% See solution above
% 0.57/0.46 % Parsed axioms : 386
% 0.57/0.46 % Removed by relevancy pruning/SinE : 263
% 0.57/0.46 % Initial clauses : 332
% 0.57/0.46 % Removed in clause preprocessing : 174
% 0.57/0.46 % Initial clauses in saturation : 158
% 0.57/0.46 % Processed clauses : 1034
% 0.57/0.46 % ...of these trivial : 14
% 0.57/0.46 % ...subsumed : 418
% 0.57/0.46 % ...remaining for further processing : 602
% 0.57/0.46 % Other redundant clauses eliminated : 28
% 0.57/0.46 % Clauses deleted for lack of memory : 0
% 0.57/0.46 % Backward-subsumed : 1
% 0.57/0.46 % Backward-rewritten : 0
% 0.57/0.46 % Generated clauses : 3065
% 0.57/0.46 % ...of the previous two non-redundant : 2869
% 0.57/0.46 % ...aggressively subsumed : 0
% 0.57/0.46 % Contextual simplify-reflections : 0
% 0.57/0.46 % Paramodulations : 3027
% 0.57/0.46 % Factorizations : 2
% 0.57/0.46 % NegExts : 0
% 0.57/0.46 % Equation resolutions : 33
% 0.57/0.46 % Disequality decompositions : 0
% 0.57/0.46 % Total rewrite steps : 979
% 0.57/0.46 % ...of those cached : 943
% 0.57/0.46 % Propositional unsat checks : 0
% 0.57/0.46 % Propositional check models : 0
% 0.57/0.46 % Propositional check unsatisfiable : 0
% 0.57/0.46 % Propositional clauses : 0
% 0.57/0.46 % Propositional clauses after purity: 0
% 0.57/0.46 % Propositional unsat core size : 0
% 0.57/0.46 % Propositional preprocessing time : 0.000
% 0.57/0.46 % Propositional encoding time : 0.000
% 0.57/0.46 % Propositional solver time : 0.000
% 0.57/0.46 % Success case prop preproc time : 0.000
% 0.57/0.46 % Success case prop encoding time : 0.000
% 0.57/0.46 % Success case prop solver time : 0.000
% 0.57/0.46 % Current number of processed clauses : 590
% 0.57/0.46 % Positive orientable unit clauses : 32
% 0.57/0.46 % Positive unorientable unit clauses: 0
% 0.57/0.46 % Negative unit clauses : 380
% 0.57/0.46 % Non-unit-clauses : 178
% 0.57/0.46 % Current number of unprocessed clauses: 1973
% 0.57/0.46 % ...number of literals in the above : 4728
% 0.57/0.46 % Current number of archived formulas : 0
% 0.57/0.46 % Current number of archived clauses : 1
% 0.57/0.46 % Clause-clause subsumption calls (NU) : 7111
% 0.57/0.46 % Rec. Clause-clause subsumption calls : 4524
% 0.57/0.46 % Non-unit clause-clause subsumptions : 312
% 0.57/0.46 % Unit Clause-clause subsumption calls : 40817
% 0.57/0.46 % Rewrite failures with RHS unbound : 0
% 0.57/0.46 % BW rewrite match attempts : 16
% 0.57/0.46 % BW rewrite match successes : 0
% 0.57/0.46 % Condensation attempts : 0
% 0.57/0.46 % Condensation successes : 0
% 0.57/0.46 % Termbank termtop insertions : 88871
% 0.57/0.46 % Search garbage collected termcells : 15366
% 0.57/0.46
% 0.57/0.46 % -------------------------------------------------
% 0.57/0.46 % User time : 0.139 s
% 0.57/0.46 % System time : 0.012 s
% 0.57/0.46 % Total time : 0.152 s
% 0.57/0.46 % Maximum resident set size: 6308 pages
% 0.57/0.46
% 0.57/0.46 % -------------------------------------------------
% 0.57/0.46 % User time : 0.149 s
% 0.57/0.46 % System time : 0.019 s
% 0.57/0.46 % Total time : 0.169 s
% 0.57/0.46 % Maximum resident set size: 5376 pages
% 0.57/0.46 % E exiting
%------------------------------------------------------------------------------