%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM698^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:16:52 AM UTC 2026
% Result : Theorem 0.24s 0.26s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 98 ( 9 ~; 5 |; 0 &; 81 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 21 ( 5 ^; 16 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
some: ( nat > $o ) > $o ).
thf(decl_26,type,
diffprop: nat > nat > nat > $o ).
thf(decl_27,type,
lessis: nat > nat > $o ).
thf(decl_28,type,
pl: nat > nat > nat ).
thf(decl_29,type,
n_1: nat ).
thf(decl_30,type,
moreis: nat > nat > $o ).
thf(satz25b,conjecture,
lessis @ ( pl @ y @ n_1 ) @ x,
file('/export/starexec/sandbox2/tmp/tmp.jCQKVGZmS8/E---3.1_3299397.p',satz25b) ).
thf(satz25,axiom,
! [X2: nat,X3: nat] :
( ( some
@ ^ [X4: nat] : ( diffprop @ X3 @ X2 @ X4 ) )
=> ( moreis @ X3 @ ( pl @ X2 @ n_1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.jCQKVGZmS8/E---3.1_3299397.p',satz25) ).
thf(satz13,axiom,
! [X2: nat,X3: nat] :
( ( moreis @ X2 @ X3 )
=> ( lessis @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.jCQKVGZmS8/E---3.1_3299397.p',satz13) ).
thf(l,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ x @ y @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.jCQKVGZmS8/E---3.1_3299397.p',l) ).
thf(c_0_4,negated_conjecture,
~ ( lessis @ ( pl @ y @ n_1 ) @ x ),
inference(assume_negation,[status(cth)],[satz25b]) ).
thf(c_0_5,plain,
! [X2: nat,X3: nat] :
( ( some
@ ^ [Z0: nat] : ( diffprop @ X3 @ X2 @ Z0 ) )
=> ( moreis @ X3 @ ( pl @ X2 @ n_1 ) ) ),
inference(fof_simplification,[status(thm)],[satz25]) ).
thf(c_0_6,negated_conjecture,
~ ( lessis @ ( pl @ y @ n_1 ) @ x ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X9: nat,X10: nat] :
( ~ ( moreis @ X9 @ X10 )
| ( lessis @ X10 @ X9 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz13])])]) ).
thf(c_0_8,plain,
! [X11: nat,X12: nat] :
( ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X12 @ X11 @ Z0 ) )
| ( moreis @ X12 @ ( pl @ X11 @ n_1 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_9,negated_conjecture,
~ ( lessis @ ( pl @ y @ n_1 ) @ x ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: nat,X2: nat] :
( ( lessis @ X2 @ X1 )
| ~ ( moreis @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X1: nat,X2: nat] :
( ( moreis @ X1 @ ( pl @ X2 @ n_1 ) )
| ~ ( some @ ( diffprop @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ x @ y @ Z0 ) ),
inference(fof_simplification,[status(thm)],[l]) ).
thf(c_0_13,negated_conjecture,
~ ( lessis @ ( pl @ y @ n_1 ) @ x ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X2: nat,X1: nat] :
( ( lessis @ ( pl @ X1 @ n_1 ) @ X2 )
| ~ ( some @ ( diffprop @ X2 @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,plain,
some @ ( diffprop @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM698^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n007.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 12:39:10 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running higher-order theorem proving
% 0.06/0.24 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.jCQKVGZmS8/E---3.1_3299397.p
% 0.24/0.26 % Version: 3.5.1-ho
% 0.24/0.26 % Preprocessing class: HSSSSMSSSSMNSFN.
% 0.24/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.26 % Starting sh5l with 300s (1) cores
% 0.24/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.26 % Starting new_bool_2 with 300s (1) cores
% 0.24/0.26 % new_bool_1 with pid 3299412 completed with status 0
% 0.24/0.26 % Result found by new_bool_1
% 0.24/0.26 % Preprocessing class: HSSSSMSSSSMNSFN.
% 0.24/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.26 % Starting sh5l with 300s (1) cores
% 0.24/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.26 % Search class: HHUNF-FFSF22-SSFFFFNN
% 0.24/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.26 % SubtermCWHack with pid 3299414 completed with status 0
% 0.24/0.26 % Result found by SubtermCWHack
% 0.24/0.26 % Preprocessing class: HSSSSMSSSSMNSFN.
% 0.24/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.24/0.26 % Starting sh5l with 300s (1) cores
% 0.24/0.26 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.26 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.26 % Search class: HHUNF-FFSF22-SSFFFFNN
% 0.24/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.26 % Preprocessing time : 0.001 s
% 0.24/0.26
% 0.24/0.26 % Proof found!
% 0.24/0.26 % SZS status Theorem
% 0.24/0.26 % SZS output start CNFRefutation
% See solution above
% 0.24/0.26 % Parsed axioms : 13
% 0.24/0.26 % Removed by relevancy pruning/SinE : 9
% 0.24/0.26 % Initial clauses : 4
% 0.24/0.26 % Removed in clause preprocessing : 0
% 0.24/0.26 % Initial clauses in saturation : 4
% 0.24/0.26 % Processed clauses : 5
% 0.24/0.26 % ...of these trivial : 0
% 0.24/0.26 % ...subsumed : 0
% 0.24/0.26 % ...remaining for further processing : 5
% 0.24/0.26 % Other redundant clauses eliminated : 0
% 0.24/0.26 % Clauses deleted for lack of memory : 0
% 0.24/0.26 % Backward-subsumed : 0
% 0.24/0.26 % Backward-rewritten : 0
% 0.24/0.26 % Generated clauses : 2
% 0.24/0.26 % ...of the previous two non-redundant : 1
% 0.24/0.26 % ...aggressively subsumed : 0
% 0.24/0.26 % Contextual simplify-reflections : 0
% 0.24/0.26 % Paramodulations : 2
% 0.24/0.26 % Factorizations : 0
% 0.24/0.26 % NegExts : 0
% 0.24/0.26 % Equation resolutions : 0
% 0.24/0.26 % Disequality decompositions : 0
% 0.24/0.26 % Total rewrite steps : 1
% 0.24/0.26 % ...of those cached : 0
% 0.24/0.26 % Propositional unsat checks : 0
% 0.24/0.26 % Propositional check models : 0
% 0.24/0.26 % Propositional check unsatisfiable : 0
% 0.24/0.26 % Propositional clauses : 0
% 0.24/0.26 % Propositional clauses after purity: 0
% 0.24/0.26 % Propositional unsat core size : 0
% 0.24/0.26 % Propositional preprocessing time : 0.000
% 0.24/0.26 % Propositional encoding time : 0.000
% 0.24/0.26 % Propositional solver time : 0.000
% 0.24/0.26 % Success case prop preproc time : 0.000
% 0.24/0.26 % Success case prop encoding time : 0.000
% 0.24/0.26 % Success case prop solver time : 0.000
% 0.24/0.26 % Current number of processed clauses : 5
% 0.24/0.26 % Positive orientable unit clauses : 1
% 0.24/0.26 % Positive unorientable unit clauses: 0
% 0.24/0.26 % Negative unit clauses : 1
% 0.24/0.26 % Non-unit-clauses : 3
% 0.24/0.26 % Current number of unprocessed clauses: 0
% 0.24/0.26 % ...number of literals in the above : 0
% 0.24/0.26 % Current number of archived formulas : 0
% 0.24/0.26 % Current number of archived clauses : 0
% 0.24/0.26 % Clause-clause subsumption calls (NU) : 1
% 0.24/0.26 % Rec. Clause-clause subsumption calls : 1
% 0.24/0.26 % Non-unit clause-clause subsumptions : 0
% 0.24/0.26 % Unit Clause-clause subsumption calls : 0
% 0.24/0.26 % Rewrite failures with RHS unbound : 0
% 0.24/0.26 % BW rewrite match attempts : 0
% 0.24/0.26 % BW rewrite match successes : 0
% 0.24/0.26 % Condensation attempts : 0
% 0.24/0.26 % Condensation successes : 0
% 0.24/0.26 % Termbank termtop insertions : 352
% 0.24/0.26 % Search garbage collected termcells : 54
% 0.24/0.26
% 0.24/0.26 % -------------------------------------------------
% 0.24/0.26 % User time : 0.002 s
% 0.24/0.26 % System time : 0.002 s
% 0.24/0.26 % Total time : 0.004 s
% 0.24/0.26 % Maximum resident set size: 3632 pages
% 0.24/0.26
% 0.24/0.26 % -------------------------------------------------
% 0.24/0.26 % User time : 0.003 s
% 0.24/0.26 % System time : 0.008 s
% 0.24/0.26 % Total time : 0.010 s
% 0.24/0.26 % Maximum resident set size: 4864 pages
% 0.24/0.26 % E exiting
%------------------------------------------------------------------------------