%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM689^1 : 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 : n026.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 08:16:50 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 144 ( 11 ~; 6 |; 0 &; 122 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 12 ^; 22 !; 0 ?; 34 :)
% 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,
u: nat ).
thf(decl_27,type,
lessis: nat > nat > $o ).
thf(decl_28,type,
some: ( nat > $o ) > $o ).
thf(decl_29,type,
diffprop: nat > nat > nat > $o ).
thf(decl_30,type,
pl: nat > nat > nat ).
thf(decl_31,type,
moreis: nat > nat > $o ).
thf(satz22c,conjecture,
( some
@ ^ [X1: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.uRca2HlmqD/E---3.1_537399.p',satz22c) ).
thf(satz22a,axiom,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( moreis @ X2 @ X3 )
=> ( ( some
@ ^ [X6: nat] : ( diffprop @ X4 @ X5 @ X6 ) )
=> ( some
@ ^ [X6: nat] : ( diffprop @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uRca2HlmqD/E---3.1_537399.p',satz22a) ).
thf(k,axiom,
( some
@ ^ [X1: nat] : ( diffprop @ u @ z @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.uRca2HlmqD/E---3.1_537399.p',k) ).
thf(satz14,axiom,
! [X2: nat,X3: nat] :
( ( lessis @ X2 @ X3 )
=> ( moreis @ X3 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.uRca2HlmqD/E---3.1_537399.p',satz14) ).
thf(l,axiom,
lessis @ x @ y,
file('/export/starexec/sandbox2/tmp/tmp.uRca2HlmqD/E---3.1_537399.p',l) ).
thf(c_0_5,negated_conjecture,
~ ( some
@ ^ [X1: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X1 ) ),
inference(assume_negation,[status(cth)],[satz22c]) ).
thf(c_0_6,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Z0 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])]) ).
thf(c_0_7,plain,
! [X2: nat,X3: nat,X4: nat,X5: nat] :
( ( moreis @ X2 @ X3 )
=> ( ( some
@ ^ [Z0: nat] : ( diffprop @ X4 @ X5 @ Z0 ) )
=> ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ X2 @ X4 ) @ ( pl @ X3 @ X5 ) @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[satz22a]) ).
thf(c_0_8,negated_conjecture,
~ ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Z0 ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X13: nat,X14: nat,X15: nat,X16: nat] :
( ~ ( moreis @ X13 @ X14 )
| ~ ( some
@ ^ [Z0: nat] : ( diffprop @ X15 @ X16 @ Z0 ) )
| ( some
@ ^ [Z0: nat] : ( diffprop @ ( pl @ X13 @ X15 ) @ ( pl @ X14 @ X16 ) @ Z0 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_10,plain,
( some
@ ^ [Z0: nat] : ( diffprop @ u @ z @ Z0 ) ),
inference(fof_simplification,[status(thm)],[k]) ).
thf(c_0_11,negated_conjecture,
~ ( some @ ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X1: nat,X2: nat,X3: nat,X4: nat] :
( ( some @ ( diffprop @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X4 ) ) )
| ~ ( moreis @ X1 @ X2 )
| ~ ( some @ ( diffprop @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
some @ ( diffprop @ u @ z ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X17: nat,X18: nat] :
( ~ ( lessis @ X17 @ X18 )
| ( moreis @ X18 @ X17 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[satz14])])]) ).
thf(c_0_15,negated_conjecture,
~ ( moreis @ y @ x ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
thf(c_0_16,plain,
! [X1: nat,X2: nat] :
( ( moreis @ X2 @ X1 )
| ~ ( lessis @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_17,plain,
lessis @ x @ y,
inference(split_conjunct,[status(thm)],[l]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM689^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:42:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.uRca2HlmqD/E---3.1_537399.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSMSSMSSSSMNSSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting sh5l with 300s (1) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % new_ho_10 with pid 537412 completed with status 0
% 0.08/0.26 % Result found by new_ho_10
% 0.08/0.26 % Preprocessing class: HSMSSMSSSSMNSSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHUNF-FFSF22-SSSFFFNN
% 0.08/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.26 % Starting new_ho_10 with 901s (1) cores
% 0.08/0.26 % Starting sh5l with 151s (1) cores
% 0.08/0.26 % Starting new_bool_1 with 151s (1) cores
% 0.08/0.26 % Starting new_bool_2 with 146s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 537416 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSMSSMSSSSMNSSN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.26 % No SInE strategy applied
% 0.08/0.26 % Search class: HHUNF-FFSF22-SSSFFFNN
% 0.08/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 15
% 0.08/0.26 % Removed by relevancy pruning/SinE : 0
% 0.08/0.26 % Initial clauses : 15
% 0.08/0.26 % Removed in clause preprocessing : 10
% 0.08/0.26 % Initial clauses in saturation : 5
% 0.08/0.26 % Processed clauses : 6
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 6
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 2
% 0.08/0.26 % ...of the previous two non-redundant : 1
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 2
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 2
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 6
% 0.08/0.26 % Positive orientable unit clauses : 2
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 2
% 0.08/0.26 % Non-unit-clauses : 2
% 0.08/0.26 % Current number of unprocessed clauses: 0
% 0.08/0.26 % ...number of literals in the above : 0
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 0
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 1
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 1
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 1
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 609
% 0.08/0.26 % Search garbage collected termcells : 85
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.003 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.006 s
% 0.08/0.26 % Maximum resident set size: 3584 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.008 s
% 0.08/0.26 % System time : 0.010 s
% 0.08/0.26 % Total time : 0.019 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------