%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM418^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:16:37 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 68 ( 5 ~; 0 |; 0 &; 63 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-4 aty)
% Number of variables : 30 ( 6 ^; 22 !; 2 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
zero: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_35,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(decl_37,type,
esk1_2: ( ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_38,type,
esk2_1: ( ( $i > $i ) > $i > $i ) > $i ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three )
= three ),
file('/export/starexec/sandbox2/tmp/tmp.2w8BgohC0B/E---3.1_6688.p',thm) ).
thf(plus_ax,axiom,
( plus
= ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ X1 @ ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2w8BgohC0B/E---3.1_6688.p',plus_ax) ).
thf(zero_ax,axiom,
( zero
= ( ^ [X1: $i > $i,X2: $i] : X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2w8BgohC0B/E---3.1_6688.p',zero_ax) ).
thf(c_0_3,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three )
= three ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_4,negated_conjecture,
! [X72: ( $i > $i ) > $i > $i] :
( ( plus @ X72 @ three )
!= three ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
thf(c_0_5,plain,
! [X31: ( $i > $i ) > $i > $i,X32: ( $i > $i ) > $i > $i,X33: $i > $i,X34: $i] :
( ( plus @ X31 @ X32 @ X33 @ X34 )
= ( X31 @ X33 @ ( X32 @ X33 @ X34 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[plus_ax])]) ).
thf(c_0_6,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three )
!= three ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X64: ( $i > $i ) > $i > $i,X65: ( $i > $i ) > $i > $i,X66: $i > $i,X67: $i] :
( ( plus @ X64 @ X65 @ X66 @ X67 )
= ( X64 @ X66 @ ( X65 @ X66 @ X67 ) ) ),
inference(variable_rename,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X6: $i > $i,X7: $i] :
( ( zero @ X6 @ X7 )
= X7 ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[zero_ax])]) ).
thf(c_0_9,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) )
!= ( three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(neg_ext,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X4: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ X3 @ X4 @ X1 @ X2 )
= ( X3 @ X1 @ ( X4 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X39: $i > $i,X40: $i] :
( ( zero @ X39 @ X40 )
= X40 ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( esk1_2 @ X3 ) @ ( three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) )
!= ( three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,plain,
! [X1: $i > $i,X2: $i] :
( ( zero @ X1 @ X2 )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_12,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM418^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n012.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 11:59:48 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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.2w8BgohC0B/E---3.1_6688.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting pre_casc_2 with 1500s (5) cores
% 0.09/0.25 % Starting sh2 with 300s (1) cores
% 0.09/0.25 % Starting sh3 with 300s (1) cores
% 0.09/0.25 % Starting new_ho_10 with 300s (1) cores
% 0.09/0.25 % pre_casc_2 with pid 6701 completed with status 0
% 0.09/0.25 % Result found by pre_casc_2
% 0.09/0.25 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting pre_casc_2 with 1500s (5) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.09/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.25 % Starting pre_casc_2 with 901s (1) cores
% 0.09/0.25 % Starting sh2 with 151s (1) cores
% 0.09/0.25 % Starting sh3 with 151s (1) cores
% 0.09/0.25 % Starting sh9 with 146s (1) cores
% 0.09/0.25 % pre_casc_2 with pid 6707 completed with status 0
% 0.09/0.25 % Result found by pre_casc_2
% 0.09/0.25 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting pre_casc_2 with 1500s (5) cores
% 0.09/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.09/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.09/0.25 % Starting pre_casc_2 with 901s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25 % Presaturation interreduction done
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 29
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 29
% 0.09/0.25 % Removed in clause preprocessing : 14
% 0.09/0.25 % Initial clauses in saturation : 15
% 0.09/0.25 % Processed clauses : 87
% 0.09/0.25 % ...of these trivial : 30
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 57
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 0
% 0.09/0.25 % Generated clauses : 1068
% 0.09/0.25 % ...of the previous two non-redundant : 1051
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 1059
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 3
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 1735
% 0.09/0.25 % ...of those cached : 1664
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 42
% 0.09/0.25 % Positive orientable unit clauses : 30
% 0.09/0.25 % Positive unorientable unit clauses: 7
% 0.09/0.25 % Negative unit clauses : 5
% 0.09/0.25 % Non-unit-clauses : 0
% 0.09/0.25 % Current number of unprocessed clauses: 991
% 0.09/0.25 % ...number of literals in the above : 991
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 15
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 10
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 600
% 0.09/0.25 % BW rewrite match successes : 4
% 0.09/0.25 % Condensation attempts : 87
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 22101
% 0.09/0.25 % Search garbage collected termcells : 87
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.020 s
% 0.09/0.25 % System time : 0.002 s
% 0.09/0.25 % Total time : 0.022 s
% 0.09/0.25 % Maximum resident set size: 3648 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.087 s
% 0.09/0.25 % System time : 0.015 s
% 0.09/0.25 % Total time : 0.102 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------