%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM635^4 : 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 : n014.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 08:16:38 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 17 ~; 5 |; 4 &; 64 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 41 ^; 12 !; 0 ?; 53 :)
% 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_48,type,
ordsucc: $i > $i ).
thf(decl_62,type,
imp: $o > $o > $o ).
thf(decl_63,type,
d_not: $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_126,type,
nis: $i > $i > $o ).
thf(decl_135,type,
esk1_0: $i ).
thf(decl_136,type,
esk2_0: $i ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X1: $i,X101: $i,X102: $i] : ( X101 = X102 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',def_e_is) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X76: $o] : ( imp @ X76 @ ~ $true ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',def_d_not) ).
thf(def_imp,axiom,
( imp
= ( ^ [X74: $o,X75: $o] :
( X74
=> X75 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',def_imp) ).
thf(def_nis,axiom,
( nis
= ( ^ [X1: $i,X165: $i] : ( d_not @ ( n_is @ X1 @ X165 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',def_nis) ).
thf(def_n_is,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',def_n_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.UhwjMXLQCL/E---3.1_2569301.p',def_all_of) ).
thf(def_is_of,axiom,
( is_of
= ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',def_is_of) ).
thf(satz1,conjecture,
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X172: $i] : ( in @ X172 @ nat )
@ ^ [X173: $i] :
( ( nis @ X1 @ X173 )
=> ( nis @ ( ordsucc @ X1 ) @ ( ordsucc @ X173 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',satz1) ).
thf(ordsucc_inj,axiom,
! [X1: $i,X43: $i] :
( ( ( ordsucc @ X1 )
= ( ordsucc @ X43 ) )
=> ( X1 = X43 ) ),
file('/export/starexec/sandbox/tmp/tmp.UhwjMXLQCL/E---3.1_2569301.p',ordsucc_inj) ).
thf(c_0_9,plain,
( e_is
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( Z1 = Z2 ) ) ),
inference(fof_simplification,[status(thm)],[def_e_is]) ).
thf(c_0_10,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_d_not]) ).
thf(c_0_11,plain,
( imp
= ( ^ [Z0: $o,Z1: $o] :
( Z0
=> Z1 ) ) ),
inference(fof_simplification,[status(thm)],[def_imp]) ).
thf(c_0_12,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(fof_simplification,[status(thm)],[def_nis]) ).
thf(c_0_13,axiom,
( n_is
= ( ^ [Z0: $i,Z1: $i] : ( Z0 = Z1 ) ) ),
inference(apply_def,[status(thm)],[def_n_is,c_0_9]) ).
thf(c_0_14,plain,
( d_not
= ( ^ [Z0: $o] :
( Z0
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,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_16,plain,
( is_of
= ( ^ [Z0: $i,Z1: $i > $o] : ( Z1 @ Z0 ) ) ),
inference(fof_simplification,[status(thm)],[def_is_of]) ).
thf(c_0_17,negated_conjecture,
~ ( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X172: $i] : ( in @ X172 @ nat )
@ ^ [X173: $i] :
( ( nis @ X1 @ X173 )
=> ( nis @ ( ordsucc @ X1 ) @ ( ordsucc @ X173 ) ) ) ) ),
inference(assume_negation,[status(cth)],[satz1]) ).
thf(c_0_18,plain,
( nis
= ( ^ [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
=> ~ $true ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
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_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
~ ! [X233: $i] :
( ( in @ X233 @ nat )
=> ! [X232: $i] :
( ( in @ X232 @ nat )
=> ( ( ( X233 = X232 )
=> ~ $true )
=> ( ( ( ordsucc @ X233 )
= ( ordsucc @ X232 ) )
=> ~ $true ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_21,plain,
! [X281: $i,X282: $i] :
( ( ( ordsucc @ X281 )
!= ( ordsucc @ X282 ) )
| ( X281 = X282 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ordsucc_inj])])]) ).
thf(c_0_22,negated_conjecture,
( ( in @ esk1_0 @ nat )
& ( in @ esk2_0 @ nat )
& ( ( esk1_0 != esk2_0 )
| ~ $true )
& ( ( ordsucc @ esk1_0 )
= ( ordsucc @ esk2_0 ) )
& $true ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
thf(c_0_23,plain,
! [X1: $i,X4: $i] :
( ( X1 = X4 )
| ( ( ordsucc @ X1 )
!= ( ordsucc @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( ordsucc @ esk1_0 )
= ( ordsucc @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_25,negated_conjecture,
( ( esk1_0 != esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i] :
( ( X1 = esk1_0 )
| ( ( ordsucc @ X1 )
!= ( ordsucc @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_27,negated_conjecture,
esk2_0 != esk1_0,
inference(cn,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM635^4 : TPTP v9.3.1. Released v7.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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 12:01:00 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.21/0.27 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.UhwjMXLQCL/E---3.1_2569301.p
% 0.21/0.31 % Version: 3.5.1-ho
% 0.21/0.31 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.21/0.31 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting lpo1_fix with 900s (3) cores
% 0.21/0.31 % Starting full_lambda_9 with 300s (1) cores
% 0.21/0.31 % Starting almost_fo_4 with 300s (1) cores
% 0.21/0.31 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.31 % Starting pre_casc_4 with 300s (1) cores
% 0.21/0.31 % Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.31 % pre_casc_4 with pid 2569318 completed with status 0
% 0.21/0.31 % Result found by pre_casc_4
% 0.21/0.31 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.21/0.31 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting lpo1_fix with 900s (3) cores
% 0.21/0.31 % Starting full_lambda_9 with 300s (1) cores
% 0.21/0.31 % Starting almost_fo_4 with 300s (1) cores
% 0.21/0.31 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.31 % Starting pre_casc_4 with 300s (1) cores
% 0.21/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.21/0.31 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.21/0.31 % Search class: HGHSM-FFMM31-DHSMMSBN
% 0.21/0.31 % partial match(2): HGHSM-FFMM31-SHSSMSBN
% 0.21/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.31 % SubtermCWHack with pid 2569320 completed with status 0
% 0.21/0.31 % Result found by SubtermCWHack
% 0.21/0.31 % Preprocessing class: HSLMSMSSLLLCHSA.
% 0.21/0.31 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.31 % Starting lpo1_fix with 900s (3) cores
% 0.21/0.31 % Starting full_lambda_9 with 300s (1) cores
% 0.21/0.31 % Starting almost_fo_4 with 300s (1) cores
% 0.21/0.31 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.31 % Starting pre_casc_4 with 300s (1) cores
% 0.21/0.31 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.21/0.31 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.21/0.31 % Search class: HGHSM-FFMM31-DHSMMSBN
% 0.21/0.31 % partial match(2): HGHSM-FFMM31-SHSSMSBN
% 0.21/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.31 % Preprocessing time : 0.003 s
% 0.21/0.31
% 0.21/0.31 % Proof found!
% 0.21/0.31 % SZS status Theorem
% 0.21/0.31 % SZS output start CNFRefutation
% See solution above
% 0.21/0.31 % Parsed axioms : 284
% 0.21/0.31 % Removed by relevancy pruning/SinE : 233
% 0.21/0.31 % Initial clauses : 86
% 0.21/0.31 % Removed in clause preprocessing : 4
% 0.21/0.31 % Initial clauses in saturation : 82
% 0.21/0.31 % Processed clauses : 49
% 0.21/0.31 % ...of these trivial : 2
% 0.21/0.31 % ...subsumed : 4
% 0.21/0.31 % ...remaining for further processing : 43
% 0.21/0.31 % Other redundant clauses eliminated : 4
% 0.21/0.31 % Clauses deleted for lack of memory : 0
% 0.21/0.31 % Backward-subsumed : 0
% 0.21/0.31 % Backward-rewritten : 0
% 0.21/0.31 % Generated clauses : 34
% 0.21/0.31 % ...of the previous two non-redundant : 23
% 0.21/0.31 % ...aggressively subsumed : 0
% 0.21/0.31 % Contextual simplify-reflections : 0
% 0.21/0.31 % Paramodulations : 28
% 0.21/0.31 % Factorizations : 0
% 0.21/0.31 % NegExts : 0
% 0.21/0.31 % Equation resolutions : 6
% 0.21/0.31 % Disequality decompositions : 0
% 0.21/0.31 % Total rewrite steps : 9
% 0.21/0.31 % ...of those cached : 2
% 0.21/0.31 % Propositional unsat checks : 0
% 0.21/0.31 % Propositional check models : 0
% 0.21/0.31 % Propositional check unsatisfiable : 0
% 0.21/0.31 % Propositional clauses : 0
% 0.21/0.31 % Propositional clauses after purity: 0
% 0.21/0.31 % Propositional unsat core size : 0
% 0.21/0.31 % Propositional preprocessing time : 0.000
% 0.21/0.31 % Propositional encoding time : 0.000
% 0.21/0.31 % Propositional solver time : 0.000
% 0.21/0.31 % Success case prop preproc time : 0.000
% 0.21/0.31 % Success case prop encoding time : 0.000
% 0.21/0.31 % Success case prop solver time : 0.000
% 0.21/0.31 % Current number of processed clauses : 43
% 0.21/0.31 % Positive orientable unit clauses : 17
% 0.21/0.31 % Positive unorientable unit clauses: 2
% 0.21/0.31 % Negative unit clauses : 8
% 0.21/0.31 % Non-unit-clauses : 16
% 0.21/0.31 % Current number of unprocessed clauses: 56
% 0.21/0.31 % ...number of literals in the above : 195
% 0.21/0.31 % Current number of archived formulas : 0
% 0.21/0.31 % Current number of archived clauses : 0
% 0.21/0.31 % Clause-clause subsumption calls (NU) : 22
% 0.21/0.31 % Rec. Clause-clause subsumption calls : 19
% 0.21/0.31 % Non-unit clause-clause subsumptions : 1
% 0.21/0.31 % Unit Clause-clause subsumption calls : 23
% 0.21/0.31 % Rewrite failures with RHS unbound : 0
% 0.21/0.31 % BW rewrite match attempts : 2
% 0.21/0.31 % BW rewrite match successes : 0
% 0.21/0.31 % Condensation attempts : 0
% 0.21/0.31 % Condensation successes : 0
% 0.21/0.31 % Termbank termtop insertions : 10226
% 0.21/0.31 % Search garbage collected termcells : 3678
% 0.21/0.31
% 0.21/0.31 % -------------------------------------------------
% 0.21/0.31 % User time : 0.011 s
% 0.21/0.31 % System time : 0.005 s
% 0.21/0.31 % Total time : 0.016 s
% 0.21/0.31 % Maximum resident set size: 4528 pages
% 0.21/0.31
% 0.21/0.31 % -------------------------------------------------
% 0.21/0.31 % User time : 0.018 s
% 0.21/0.31 % System time : 0.010 s
% 0.21/0.31 % Total time : 0.029 s
% 0.21/0.31 % Maximum resident set size: 5120 pages
% 0.21/0.31 % E exiting
%------------------------------------------------------------------------------