%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM667^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 24 ~; 13 |; 2 &; 60 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 ^; 13 !; 0 ?; 13 :)
% 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,
less: nat > nat > $o ).
thf(satz16b,axiom,
! [X2: nat,X3: nat,X4: nat] :
( ( less @ X2 @ X3 )
=> ( ( ~ ( less @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( less @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.T2onNvBNRs/E---3.1_1211837.p',satz16b) ).
thf(l,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/tmp/tmp.T2onNvBNRs/E---3.1_1211837.p',l) ).
thf(satz17,conjecture,
( ~ ( less @ x @ z )
=> ( x = z ) ),
file('/export/starexec/sandbox/tmp/tmp.T2onNvBNRs/E---3.1_1211837.p',satz17) ).
thf(k,axiom,
( ~ ( less @ y @ z )
=> ( y = z ) ),
file('/export/starexec/sandbox/tmp/tmp.T2onNvBNRs/E---3.1_1211837.p',k) ).
thf(c_0_4,plain,
! [X2: nat,X3: nat,X4: nat] :
( ( less @ X2 @ X3 )
=> ( ( ~ ( less @ X3 @ X4 )
=> ( X3 = X4 ) )
=> ( less @ X2 @ X4 ) ) ),
inference(fof_simplification,[status(thm)],[satz16b]) ).
thf(c_0_5,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(fof_simplification,[status(thm)],[l]) ).
thf(c_0_6,negated_conjecture,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(assume_negation,[status(cth)],[satz17]) ).
thf(c_0_7,plain,
! [X15: nat,X16: nat,X17: nat] :
( ( ~ ( less @ X16 @ X17 )
| ( less @ X15 @ X17 )
| ~ ( less @ X15 @ X16 ) )
& ( ( X16 != X17 )
| ( less @ X15 @ X17 )
| ~ ( less @ X15 @ X16 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
thf(c_0_8,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
( ~ ( less @ y @ z )
=> ( y = z ) ),
inference(fof_simplification,[status(thm)],[k]) ).
thf(c_0_10,negated_conjecture,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
! [X4: nat,X3: nat,X2: nat] :
( ( less @ X4 @ X3 )
| ~ ( less @ X2 @ X3 )
| ~ ( less @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
( ( less @ y @ z )
| ( y = z ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ~ ( less @ x @ z )
& ( x != z ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
thf(c_0_15,plain,
! [X2: nat] :
( ( x = y )
| ( less @ x @ X2 )
| ~ ( less @ y @ X2 ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,plain,
( ( less @ y @ z )
| ( y = z ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
~ ( less @ x @ z ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
( ( z = y )
| ( x = y ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
thf(c_0_19,negated_conjecture,
x != z,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_20,negated_conjecture,
x = y,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_12]) ).
thf(c_0_21,negated_conjecture,
z != y,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
~ ( less @ y @ z ),
inference(rw,[status(thm)],[c_0_17,c_0_20]) ).
thf(c_0_23,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_16,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM667^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.15 % Computer : n002.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Sep 29 12:36:07 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running higher-order theorem proving
% 0.10/0.21 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.T2onNvBNRs/E---3.1_1211837.p
% 0.10/0.22 % Version: 3.5.1-ho
% 0.10/0.22 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.22 % Starting ho_unfolding_6 with 300s (1) cores
% 0.10/0.22 % Starting sh4l with 300s (1) cores
% 0.10/0.22 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.10/0.22 % new_ho_10 with pid 1211867 completed with status 0
% 0.10/0.22 % Result found by new_ho_10
% 0.10/0.22 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.22 % No SInE strategy applied
% 0.10/0.22 % Search class: HGUSF-FFSF00-SFFFFFNN
% 0.10/0.22 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.22 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.22 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.22 % Starting ehoh_best8_lambda with 151s (1) cores
% 0.10/0.22 % Starting ho_unfolding_6 with 151s (1) cores
% 0.10/0.22 % Starting sh4l with 146s (1) cores
% 0.10/0.22 % sh4l with pid 1211875 completed with status 0
% 0.10/0.22 % Result found by sh4l
% 0.10/0.22 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.10/0.22 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.22 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.22 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.22 % No SInE strategy applied
% 0.10/0.22 % Search class: HGUSF-FFSF00-SFFFFFNN
% 0.10/0.22 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.22 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.22 % Starting new_ho_10 with 901s (1) cores
% 0.10/0.22 % Starting ehoh_best8_lambda with 151s (1) cores
% 0.10/0.22 % Starting ho_unfolding_6 with 151s (1) cores
% 0.10/0.22 % Starting sh4l with 146s (1) cores
% 0.10/0.22 % Preprocessing time : 0.001 s
% 0.10/0.22
% 0.10/0.22 % Proof found!
% 0.10/0.22 % SZS status Theorem
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22 % Parsed axioms : 11
% 0.10/0.22 % Removed by relevancy pruning/SinE : 0
% 0.10/0.22 % Initial clauses : 14
% 0.10/0.22 % Removed in clause preprocessing : 8
% 0.10/0.22 % Initial clauses in saturation : 6
% 0.10/0.22 % Processed clauses : 13
% 0.10/0.22 % ...of these trivial : 0
% 0.10/0.22 % ...subsumed : 1
% 0.10/0.22 % ...remaining for further processing : 11
% 0.10/0.22 % Other redundant clauses eliminated : 0
% 0.10/0.22 % Clauses deleted for lack of memory : 0
% 0.10/0.22 % Backward-subsumed : 0
% 0.10/0.22 % Backward-rewritten : 5
% 0.10/0.22 % Generated clauses : 6
% 0.10/0.22 % ...of the previous two non-redundant : 7
% 0.10/0.22 % ...aggressively subsumed : 0
% 0.10/0.22 % Contextual simplify-reflections : 1
% 0.10/0.22 % Paramodulations : 5
% 0.10/0.22 % Factorizations : 0
% 0.10/0.22 % NegExts : 0
% 0.10/0.22 % Equation resolutions : 0
% 0.10/0.22 % Disequality decompositions : 0
% 0.10/0.22 % Total rewrite steps : 7
% 0.10/0.22 % ...of those cached : 6
% 0.10/0.22 % Propositional unsat checks : 0
% 0.10/0.22 % Propositional check models : 0
% 0.10/0.22 % Propositional check unsatisfiable : 0
% 0.10/0.22 % Propositional clauses : 0
% 0.10/0.22 % Propositional clauses after purity: 0
% 0.10/0.22 % Propositional unsat core size : 0
% 0.10/0.22 % Propositional preprocessing time : 0.000
% 0.10/0.22 % Propositional encoding time : 0.000
% 0.10/0.22 % Propositional solver time : 0.000
% 0.10/0.22 % Success case prop preproc time : 0.000
% 0.10/0.22 % Success case prop encoding time : 0.000
% 0.10/0.22 % Success case prop solver time : 0.000
% 0.10/0.22 % Current number of processed clauses : 5
% 0.10/0.22 % Positive orientable unit clauses : 1
% 0.10/0.22 % Positive unorientable unit clauses: 0
% 0.10/0.22 % Negative unit clauses : 2
% 0.10/0.22 % Non-unit-clauses : 2
% 0.10/0.22 % Current number of unprocessed clauses: 0
% 0.10/0.22 % ...number of literals in the above : 0
% 0.10/0.22 % Current number of archived formulas : 0
% 0.10/0.22 % Current number of archived clauses : 6
% 0.10/0.22 % Clause-clause subsumption calls (NU) : 6
% 0.10/0.22 % Rec. Clause-clause subsumption calls : 4
% 0.10/0.22 % Non-unit clause-clause subsumptions : 2
% 0.10/0.22 % Unit Clause-clause subsumption calls : 2
% 0.10/0.22 % Rewrite failures with RHS unbound : 0
% 0.10/0.22 % BW rewrite match attempts : 1
% 0.10/0.22 % BW rewrite match successes : 1
% 0.10/0.22 % Condensation attempts : 13
% 0.10/0.22 % Condensation successes : 0
% 0.10/0.22 % Termbank termtop insertions : 731
% 0.10/0.22 % Search garbage collected termcells : 116
% 0.10/0.22
% 0.10/0.22 % -------------------------------------------------
% 0.10/0.22 % User time : 0.003 s
% 0.10/0.22 % System time : 0.001 s
% 0.10/0.22 % Total time : 0.004 s
% 0.10/0.22 % Maximum resident set size: 3636 pages
% 0.10/0.22
% 0.10/0.22 % -------------------------------------------------
% 0.10/0.22 % User time : 0.011 s
% 0.10/0.22 % System time : 0.009 s
% 0.10/0.22 % Total time : 0.020 s
% 0.10/0.22 % Maximum resident set size: 4864 pages
% 0.10/0.22 % E exiting
%------------------------------------------------------------------------------