%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM827^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 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 08:17:11 AM UTC 2026
% Result : Theorem 1.15s 0.38s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 40 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 207 ( 12 ~; 10 |; 12 &; 163 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 7 ^; 36 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
n: $tType ).
thf(decl_23,type,
c0: n ).
thf(decl_24,type,
cS: n > n ).
thf(decl_25,type,
c_plus: n > n > n ).
thf(decl_26,type,
cPA_1: $o ).
thf(decl_27,type,
cPA_2: $o ).
thf(decl_28,type,
cPA_IND_EQ: $o ).
thf(decl_29,type,
esk1_2: ( n > n ) > ( n > n ) > n ).
thf(decl_30,type,
esk2_0: n ).
thf(cPA_THM2,conjecture,
( ( cPA_1
& cPA_2
& cPA_IND_EQ )
=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= ( c_plus @ c0 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cGiI59MSlt/E---3.1_1209184.p',cPA_THM2) ).
thf(cPA_1_def,axiom,
( cPA_1
<=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.cGiI59MSlt/E---3.1_1209184.p',cPA_1_def) ).
thf(cPA_2_def,axiom,
( cPA_2
<=> ! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cGiI59MSlt/E---3.1_1209184.p',cPA_2_def) ).
thf(cPA_IND_EQ_def,axiom,
( cPA_IND_EQ
<=> ! [X3: n > n,X4: n > n] :
( ( ( ( X3 @ c0 )
= ( X4 @ c0 ) )
& ! [X1: n] :
( ( ( X3 @ X1 )
= ( X4 @ X1 ) )
=> ( ( X3 @ ( cS @ X1 ) )
= ( X4 @ ( cS @ X1 ) ) ) ) )
=> ! [X1: n] :
( ( X3 @ X1 )
= ( X4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cGiI59MSlt/E---3.1_1209184.p',cPA_IND_EQ_def) ).
thf(c_0_4,negated_conjecture,
~ ( ( cPA_1
& cPA_2
& cPA_IND_EQ )
=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= ( c_plus @ c0 @ X1 ) ) ),
inference(assume_negation,[status(cth)],[cPA_THM2]) ).
thf(c_0_5,negated_conjecture,
~ ( ( ! [X13: n] :
( ( c_plus @ X13 @ c0 )
= X13 )
& ! [X14: n,X15: n] :
( ( c_plus @ X14 @ ( cS @ X15 ) )
= ( cS @ ( c_plus @ X14 @ X15 ) ) )
& ! [X16: n > n,X17: n > n] :
( ( ( ( X16 @ c0 )
= ( X17 @ c0 ) )
& ! [X18: n] :
( ( ( X16 @ X18 )
= ( X17 @ X18 ) )
=> ( ( X16 @ ( cS @ X18 ) )
= ( X17 @ ( cS @ X18 ) ) ) ) )
=> ! [X19: n] :
( ( X16 @ X19 )
= ( X17 @ X19 ) ) ) )
=> ! [X1: n] :
( ( c_plus @ X1 @ c0 )
= ( c_plus @ c0 @ X1 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,cPA_1_def]),cPA_2_def]),cPA_IND_EQ_def]) ).
thf(c_0_6,negated_conjecture,
! [X20: n,X21: n,X22: n,X23: n > n,X24: n > n,X26: n] :
( ( ( c_plus @ X20 @ c0 )
= X20 )
& ( ( c_plus @ X21 @ ( cS @ X22 ) )
= ( cS @ ( c_plus @ X21 @ X22 ) ) )
& ( ( ( X23 @ ( esk1_2 @ X23 @ X24 ) )
= ( X24 @ ( esk1_2 @ X23 @ X24 ) ) )
| ( ( X23 @ c0 )
!= ( X24 @ c0 ) )
| ( ( X23 @ X26 )
= ( X24 @ X26 ) ) )
& ( ( ( X23 @ ( cS @ ( esk1_2 @ X23 @ X24 ) ) )
!= ( X24 @ ( cS @ ( esk1_2 @ X23 @ X24 ) ) ) )
| ( ( X23 @ c0 )
!= ( X24 @ c0 ) )
| ( ( X23 @ X26 )
= ( X24 @ X26 ) ) )
& ( ( c_plus @ esk2_0 @ c0 )
!= ( c_plus @ c0 @ esk2_0 ) ) ),
inference(distribute,[status(thm)],[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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: n,X3: n > n,X4: n > n] :
( ( ( X3 @ ( esk1_2 @ X3 @ X4 ) )
= ( X4 @ ( esk1_2 @ X3 @ X4 ) ) )
| ( ( X3 @ X1 )
= ( X4 @ X1 ) )
| ( ( X3 @ c0 )
!= ( X4 @ c0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X1: n] :
( ( c_plus @ X1 @ c0 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: n,X3: n > n,X4: n > n] :
( ( ( X3
@ ( esk1_2 @ X3
@ ^ [Z0: n] : ( c_plus @ ( X4 @ Z0 ) @ Z0 ) ) )
= ( c_plus
@ ( X4
@ ( esk1_2 @ X3
@ ^ [Z0: n] : ( c_plus @ ( X4 @ Z0 ) @ Z0 ) ) )
@ ( esk1_2 @ X3
@ ^ [Z0: n] : ( c_plus @ ( X4 @ Z0 ) @ Z0 ) ) ) )
| ( ( X3 @ X1 )
= ( c_plus @ ( X4 @ X1 ) @ X1 ) )
| ( ( X3 @ c0 )
!= ( X4 @ c0 ) ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: n,X2: n] :
( ( c_plus @ X1 @ ( cS @ X2 ) )
= ( cS @ ( c_plus @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
( ( c_plus @ c0
@ ( esk1_2
@ ^ [Z0: n] : Z0
@ ( c_plus @ c0 ) ) )
= ( esk1_2
@ ^ [Z0: n] : Z0
@ ( c_plus @ c0 ) ) ),
inference(condense,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
thf(c_0_12,negated_conjecture,
( ( c_plus @ esk2_0 @ c0 )
!= ( c_plus @ c0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
! [X1: n,X3: n > n,X4: n > n] :
( ( ( X3 @ X1 )
= ( X4 @ X1 ) )
| ( ( X3 @ ( cS @ ( esk1_2 @ X3 @ X4 ) ) )
!= ( X4 @ ( cS @ ( esk1_2 @ X3 @ X4 ) ) ) )
| ( ( X3 @ c0 )
!= ( X4 @ c0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
( ( c_plus @ c0
@ ( cS
@ ( esk1_2
@ ^ [Z0: n] : Z0
@ ( c_plus @ c0 ) ) ) )
= ( cS
@ ( esk1_2
@ ^ [Z0: n] : Z0
@ ( c_plus @ c0 ) ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ( c_plus @ c0 @ esk2_0 )
!= esk2_0 ),
inference(rw,[status(thm)],[c_0_12,c_0_8]) ).
thf(c_0_16,negated_conjecture,
! [X1: n] :
( ( c_plus @ c0 @ X1 )
= X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_8])]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM827^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n001.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 13:09:20 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
% 0.07/0.24 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.cGiI59MSlt/E---3.1_1209184.p
% 1.15/0.38 % Version: 3.5.1-ho
% 1.15/0.38 % Preprocessing class: HSSSSLSSSLSNSFA.
% 1.15/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.38 % Starting post_as_ho5 with 1500s (5) cores
% 1.15/0.38 % Starting post_as_ho10 with 300s (1) cores
% 1.15/0.38 % Starting post_as_ho4 with 300s (1) cores
% 1.15/0.38 % Starting sh5l with 300s (1) cores
% 1.15/0.38 % post_as_ho5 with pid 1209197 completed with status 0
% 1.15/0.38 % Result found by post_as_ho5
% 1.15/0.38 % Preprocessing class: HSSSSLSSSLSNSFA.
% 1.15/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.38 % Starting post_as_ho5 with 1500s (5) cores
% 1.15/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 1.15/0.38 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 1.15/0.38 % Search class: HGUPS-FFSF21-MSFFMSNN
% 1.15/0.38 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.15/0.38 % Starting SubtermCWHack with 151s (1) cores
% 1.15/0.38 % Starting post_as_ho10 with 500s (1) cores
% 1.15/0.38 % Starting post_as_ho5 with 251s (1) cores
% 1.15/0.38 % Starting post_as_ho4 with 251s (1) cores
% 1.15/0.38 % Starting new_ho_10_unif with 251s (1) cores
% 1.15/0.38 % new_ho_10_unif with pid 1209208 completed with status 0
% 1.15/0.38 % Result found by new_ho_10_unif
% 1.15/0.38 % Preprocessing class: HSSSSLSSSLSNSFA.
% 1.15/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.38 % Starting post_as_ho5 with 1500s (5) cores
% 1.15/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 1.15/0.38 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 1.15/0.38 % Search class: HGUPS-FFSF21-MSFFMSNN
% 1.15/0.38 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.15/0.38 % Starting SubtermCWHack with 151s (1) cores
% 1.15/0.38 % Starting post_as_ho10 with 500s (1) cores
% 1.15/0.38 % Starting post_as_ho5 with 251s (1) cores
% 1.15/0.38 % Starting post_as_ho4 with 251s (1) cores
% 1.15/0.38 % Starting new_ho_10_unif with 251s (1) cores
% 1.15/0.38 % Preprocessing time : 0.001 s
% 1.15/0.38 % Presaturation interreduction done
% 1.15/0.38
% 1.15/0.38 % Proof found!
% 1.15/0.38 % SZS status Theorem
% 1.15/0.38 % SZS output start CNFRefutation
% See solution above
% 1.15/0.38 % Parsed axioms : 11
% 1.15/0.38 % Removed by relevancy pruning/SinE : 7
% 1.15/0.38 % Initial clauses : 5
% 1.15/0.38 % Removed in clause preprocessing : 0
% 1.15/0.38 % Initial clauses in saturation : 5
% 1.15/0.38 % Processed clauses : 118
% 1.15/0.38 % ...of these trivial : 8
% 1.15/0.38 % ...subsumed : 17
% 1.15/0.38 % ...remaining for further processing : 93
% 1.15/0.38 % Other redundant clauses eliminated : 64
% 1.15/0.38 % Clauses deleted for lack of memory : 0
% 1.15/0.38 % Backward-subsumed : 3
% 1.15/0.38 % Backward-rewritten : 18
% 1.15/0.38 % Generated clauses : 1472
% 1.15/0.38 % ...of the previous two non-redundant : 1125
% 1.15/0.38 % ...aggressively subsumed : 0
% 1.15/0.38 % Contextual simplify-reflections : 0
% 1.15/0.38 % Paramodulations : 1179
% 1.15/0.38 % Factorizations : 9
% 1.15/0.38 % NegExts : 0
% 1.15/0.38 % Equation resolutions : 284
% 1.15/0.38 % Disequality decompositions : 0
% 1.15/0.38 % Total rewrite steps : 785
% 1.15/0.38 % ...of those cached : 599
% 1.15/0.38 % Propositional unsat checks : 0
% 1.15/0.38 % Propositional check models : 0
% 1.15/0.38 % Propositional check unsatisfiable : 0
% 1.15/0.38 % Propositional clauses : 0
% 1.15/0.38 % Propositional clauses after purity: 0
% 1.15/0.38 % Propositional unsat core size : 0
% 1.15/0.38 % Propositional preprocessing time : 0.000
% 1.15/0.38 % Propositional encoding time : 0.000
% 1.15/0.38 % Propositional solver time : 0.000
% 1.15/0.38 % Success case prop preproc time : 0.000
% 1.15/0.38 % Success case prop encoding time : 0.000
% 1.15/0.38 % Success case prop solver time : 0.000
% 1.15/0.38 % Current number of processed clauses : 67
% 1.15/0.38 % Positive orientable unit clauses : 20
% 1.15/0.38 % Positive unorientable unit clauses: 0
% 1.15/0.38 % Negative unit clauses : 0
% 1.15/0.38 % Non-unit-clauses : 47
% 1.15/0.38 % Current number of unprocessed clauses: 943
% 1.15/0.38 % ...number of literals in the above : 2756
% 1.15/0.38 % Current number of archived formulas : 0
% 1.15/0.38 % Current number of archived clauses : 26
% 1.15/0.38 % Clause-clause subsumption calls (NU) : 368
% 1.15/0.38 % Rec. Clause-clause subsumption calls : 368
% 1.15/0.38 % Non-unit clause-clause subsumptions : 19
% 1.15/0.38 % Unit Clause-clause subsumption calls : 30
% 1.15/0.38 % Rewrite failures with RHS unbound : 0
% 1.15/0.38 % BW rewrite match attempts : 70
% 1.15/0.38 % BW rewrite match successes : 22
% 1.15/0.38 % Condensation attempts : 118
% 1.15/0.38 % Condensation successes : 16
% 1.15/0.38 % Termbank termtop insertions : 249192
% 1.15/0.38 % Search garbage collected termcells : 209
% 1.15/0.38
% 1.15/0.38 % -------------------------------------------------
% 1.15/0.38 % User time : 0.083 s
% 1.15/0.38 % System time : 0.012 s
% 1.15/0.38 % Total time : 0.095 s
% 1.15/0.38 % Maximum resident set size: 3636 pages
% 1.15/0.38
% 1.15/0.38 % -------------------------------------------------
% 1.15/0.38 % User time : 0.509 s
% 1.15/0.38 % System time : 0.057 s
% 1.15/0.38 % Total time : 0.566 s
% 1.15/0.38 % Maximum resident set size: 4864 pages
% 1.15/0.38 % E exiting
%------------------------------------------------------------------------------