%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM666^1 : 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 : n012.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 08:16:45 AM UTC 2026
% Result : Theorem 0.09s 0.14s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 119 ( 12 ~; 8 |; 0 &; 94 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 12 ^; 20 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
y: nat ).
thf(decl_25,type,
z: nat ).
thf(decl_26,type,
some: ( nat > $o ) > $o ).
thf(decl_27,type,
diffprop: nat > nat > nat > $o ).
thf(decl_28,type,
moreis: nat > nat > $o ).
thf(decl_29,type,
lessis: nat > nat > $o ).
thf(satz16a,axiom,
! [X2: nat,X3: nat,X4: nat] :
( ( lessis @ X2 @ X3 )
=> ( ( some
@ ^ [X5: nat] : ( diffprop @ X4 @ X3 @ X5 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ X4 @ X2 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vH7HYuDjUb/E---3.1_37243.p',satz16a) ).
thf(m,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ x @ y @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vH7HYuDjUb/E---3.1_37243.p',m) ).
thf(satz16d,conjecture,
( some
@ ^ [X1: nat] : ( diffprop @ x @ z @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vH7HYuDjUb/E---3.1_37243.p',satz16d) ).
thf(satz13,axiom,
! [X2: nat,X3: nat] :
( ( moreis @ X2 @ X3 )
=> ( lessis @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vH7HYuDjUb/E---3.1_37243.p',satz13) ).
thf(n,axiom,
moreis @ y @ z,
file('/export/starexec/sandbox2/tmp/tmp.vH7HYuDjUb/E---3.1_37243.p',n) ).
thf(c_0_5,plain,
! [X2: nat,X3: nat,X4: nat] :
( ( lessis @ X2 @ X3 )
=> ( ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X3 @ Z0 ) )
=> ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X2 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz16a]) ).
thf(c_0_6,plain,
! [X11: nat,X12: nat,X13: nat] :
( ~ ( lessis @ X11 @ X12 )
| ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X13 @ X12 @ Z0 ) )
| ( some
@ ^ [Z0: nat] : ( diffprop @ X13 @ X11 @ Z0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_7,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ x @ y @ Z0 ) ),
inference(fof_simplification,[status(thm)],[m]) ).
thf(c_0_8,negated_conjecture,
~ ( some
@ ^ [X1: nat] : ( diffprop @ x @ z @ X1 ) ),
inference(assume_negation,[status(cth)],[satz16d]) ).
thf(c_0_9,plain,
! [X1: nat,X3: nat,X2: nat] :
( ( some @ ( diffprop @ X3 @ X1 ) )
| ~ ( lessis @ X1 @ X2 )
| ~ ( some @ ( diffprop @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
some @ ( diffprop @ x @ y ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X14: nat,X15: nat] :
( ~ ( moreis @ X14 @ X15 )
| ( lessis @ X15 @ X14 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz13])])]) ).
thf(c_0_12,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ x @ z @ Z0 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])]) ).
thf(c_0_13,plain,
! [X1: nat] :
( ( some @ ( diffprop @ x @ X1 ) )
| ~ ( lessis @ X1 @ y ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_14,plain,
! [X1: nat,X2: nat] :
( ( lessis @ X2 @ X1 )
| ~ ( moreis @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ x @ z @ Z0 ) ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
! [X1: nat] :
( ( some @ ( diffprop @ x @ X1 ) )
| ~ ( moreis @ y @ X1 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
moreis @ y @ z,
inference(split_conjunct,[status(thm)],[n]) ).
thf(c_0_18,negated_conjecture,
~ ( some @ ( diffprop @ x @ z ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_19,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM666^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 12:33:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running higher-order theorem proving
% 0.09/0.13 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.vH7HYuDjUb/E---3.1_37243.p
% 0.09/0.14 % Version: 3.5.1-ho
% 0.09/0.14 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.09/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.14 % Starting sh3 with 1500s (5) cores
% 0.09/0.14 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.14 % Starting sh2lt with 300s (1) cores
% 0.09/0.14 % Starting ho_unfolding_1 with 300s (1) cores
% 0.09/0.14 % ehoh_best8_lambda with pid 37258 completed with status 0
% 0.09/0.14 % Result found by ehoh_best8_lambda
% 0.09/0.14 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.09/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.14 % Starting sh3 with 1500s (5) cores
% 0.09/0.14 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.09/0.14 % No SInE strategy applied
% 0.09/0.14 % Search class: HHUNF-FFSF00-SSSFFFNN
% 0.09/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.14 % SubtermCWHack with pid 37261 completed with status 0
% 0.09/0.14 % Result found by SubtermCWHack
% 0.09/0.14 % Preprocessing class: HSSSSMSSSSMNSSN.
% 0.09/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.14 % Starting sh3 with 1500s (5) cores
% 0.09/0.14 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = Auto)
% 0.09/0.14 % No SInE strategy applied
% 0.09/0.14 % Search class: HHUNF-FFSF00-SSSFFFNN
% 0.09/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.14 % Preprocessing time : 0.001 s
% 0.09/0.14
% 0.09/0.14 % Proof found!
% 0.09/0.14 % SZS status Theorem
% 0.09/0.14 % SZS output start CNFRefutation
% See solution above
% 0.09/0.15 % Parsed axioms : 13
% 0.09/0.15 % Removed by relevancy pruning/SinE : 0
% 0.09/0.15 % Initial clauses : 13
% 0.09/0.15 % Removed in clause preprocessing : 8
% 0.09/0.15 % Initial clauses in saturation : 5
% 0.09/0.15 % Processed clauses : 7
% 0.09/0.15 % ...of these trivial : 0
% 0.09/0.15 % ...subsumed : 0
% 0.09/0.15 % ...remaining for further processing : 7
% 0.09/0.15 % Other redundant clauses eliminated : 0
% 0.09/0.15 % Clauses deleted for lack of memory : 0
% 0.09/0.15 % Backward-subsumed : 0
% 0.09/0.15 % Backward-rewritten : 0
% 0.09/0.15 % Generated clauses : 3
% 0.09/0.15 % ...of the previous two non-redundant : 2
% 0.09/0.15 % ...aggressively subsumed : 0
% 0.09/0.15 % Contextual simplify-reflections : 0
% 0.09/0.15 % Paramodulations : 3
% 0.09/0.15 % Factorizations : 0
% 0.09/0.15 % NegExts : 0
% 0.09/0.15 % Equation resolutions : 0
% 0.09/0.15 % Disequality decompositions : 0
% 0.09/0.15 % Total rewrite steps : 0
% 0.09/0.15 % ...of those cached : 0
% 0.09/0.15 % Propositional unsat checks : 0
% 0.09/0.15 % Propositional check models : 0
% 0.09/0.15 % Propositional check unsatisfiable : 0
% 0.09/0.15 % Propositional clauses : 0
% 0.09/0.15 % Propositional clauses after purity: 0
% 0.09/0.15 % Propositional unsat core size : 0
% 0.09/0.15 % Propositional preprocessing time : 0.000
% 0.09/0.15 % Propositional encoding time : 0.000
% 0.09/0.15 % Propositional solver time : 0.000
% 0.09/0.15 % Success case prop preproc time : 0.000
% 0.09/0.15 % Success case prop encoding time : 0.000
% 0.09/0.15 % Success case prop solver time : 0.000
% 0.09/0.15 % Current number of processed clauses : 7
% 0.09/0.15 % Positive orientable unit clauses : 2
% 0.09/0.15 % Positive unorientable unit clauses: 0
% 0.09/0.15 % Negative unit clauses : 1
% 0.09/0.15 % Non-unit-clauses : 4
% 0.09/0.15 % Current number of unprocessed clauses: 0
% 0.09/0.15 % ...number of literals in the above : 0
% 0.09/0.15 % Current number of archived formulas : 0
% 0.09/0.15 % Current number of archived clauses : 0
% 0.09/0.15 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.15 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.15 % Non-unit clause-clause subsumptions : 0
% 0.09/0.15 % Unit Clause-clause subsumption calls : 0
% 0.09/0.15 % Rewrite failures with RHS unbound : 0
% 0.09/0.15 % BW rewrite match attempts : 0
% 0.09/0.15 % BW rewrite match successes : 0
% 0.09/0.15 % Condensation attempts : 0
% 0.09/0.15 % Condensation successes : 0
% 0.09/0.15 % Termbank termtop insertions : 576
% 0.09/0.15 % Search garbage collected termcells : 79
% 0.09/0.15
% 0.09/0.15 % -------------------------------------------------
% 0.09/0.15 % User time : 0.003 s
% 0.09/0.15 % System time : 0.000 s
% 0.09/0.15 % Total time : 0.003 s
% 0.09/0.15 % Maximum resident set size: 3636 pages
% 0.09/0.15
% 0.09/0.15 % -------------------------------------------------
% 0.09/0.15 % User time : 0.003 s
% 0.09/0.15 % System time : 0.004 s
% 0.09/0.15 % Total time : 0.007 s
% 0.09/0.15 % Maximum resident set size: 4608 pages
% 0.09/0.15 % E exiting
%------------------------------------------------------------------------------