%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM798^1 : 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 08:17:09 AM UTC 2026
% Result : Theorem 0.13s 0.26s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 70 ( 6 ~; 0 |; 0 &; 64 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-4 aty)
% Number of variables : 32 ( 6 ^; 24 !; 2 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
one: ( $i > $i ) > $i > $i ).
thf(decl_36,type,
mult: ( ( $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_39,type,
esk3_1: ( ( $i > $i ) > $i > $i ) > $i ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vj5NhULXrh/E---3.1_1237344.p',one_ax) ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ one )
= one ),
file('/export/starexec/sandbox/tmp/tmp.Vj5NhULXrh/E---3.1_1237344.p',thm) ).
thf(mult_ax,axiom,
( mult
= ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Vj5NhULXrh/E---3.1_1237344.p',mult_ax) ).
thf(c_0_3,plain,
! [X8: $i > $i,X9: $i] :
( ( one @ X8 @ X9 )
= ( X8 @ X9 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).
thf(c_0_4,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ one )
= one ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_5,plain,
! [X41: $i > $i,X42: $i] :
( ( one @ X41 @ X42 )
= ( X41 @ X42 ) ),
inference(variable_rename,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X72: ( $i > $i ) > $i > $i] :
( ( mult @ X72 @ one )
!= one ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ one )
!= one ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: $i > $i] :
( ( one @ X1 )
= X1 ),
inference(pos_ext,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X35: ( $i > $i ) > $i > $i,X36: ( $i > $i ) > $i > $i,X37: $i > $i,X38: $i] :
( ( mult @ X35 @ X36 @ X37 @ X38 )
= ( X35 @ ( X36 @ X37 ) @ X38 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).
thf(c_0_11,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ one @ ( esk1_2 @ X3 ) )
!= ( esk1_2 @ X3 ) ),
inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_8]),c_0_9]) ).
thf(c_0_12,plain,
! [X68: ( $i > $i ) > $i > $i,X69: ( $i > $i ) > $i > $i,X70: $i > $i,X71: $i] :
( ( mult @ X68 @ X69 @ X70 @ X71 )
= ( X68 @ ( X69 @ X70 ) @ X71 ) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ one @ ( esk1_2 @ X3 ) @ ( esk3_1 @ X3 ) )
!= ( esk1_2 @ X3 @ ( esk3_1 @ X3 ) ) ),
inference(neg_ext,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( mult @ X3 @ X4 @ X1 @ X2 )
= ( X3 @ ( X4 @ X1 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( esk1_2 @ X3 ) @ ( esk3_1 @ X3 ) )
!= ( esk1_2 @ X3 @ ( esk3_1 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_9]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_15,c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM798^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.16 % Computer : n002.cluster.edu
% 0.13/0.16 % Model : x86_64 x86_64
% 0.13/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.16 % Memory : 8046.5625MB
% 0.13/0.16 % OS : Linux 6.8.0-71-generic
% 0.13/0.16 % CPULimit : 300
% 0.13/0.16 % WCLimit : 300
% 0.13/0.16 % DateTime : Tue Sep 29 13:02:52 UTC 2026
% 0.13/0.16 % CPUTime :
% 0.13/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.21 Running higher-order theorem proving
% 0.13/0.22 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.Vj5NhULXrh/E---3.1_1237344.p
% 0.13/0.26 % Version: 3.5.1-ho
% 0.13/0.26 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.13/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.26 % Starting pre_casc_2 with 1500s (5) cores
% 0.13/0.26 % Starting sh2 with 300s (1) cores
% 0.13/0.26 % Starting sh3 with 300s (1) cores
% 0.13/0.26 % Starting new_ho_10 with 300s (1) cores
% 0.13/0.26 % pre_casc_2 with pid 1237372 completed with status 0
% 0.13/0.26 % Result found by pre_casc_2
% 0.13/0.26 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.13/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.26 % Starting pre_casc_2 with 1500s (5) cores
% 0.13/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.26 % No SInE strategy applied
% 0.13/0.26 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.13/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.13/0.26 % Starting pre_casc_2 with 901s (1) cores
% 0.13/0.26 % Starting sh2 with 151s (1) cores
% 0.13/0.26 % Starting sh3 with 151s (1) cores
% 0.13/0.26 % Starting sh9 with 146s (1) cores
% 0.13/0.26 % sh2 with pid 1237378 completed with status 0
% 0.13/0.26 % Result found by sh2
% 0.13/0.26 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.13/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.26 % Starting pre_casc_2 with 1500s (5) cores
% 0.13/0.26 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.26 % No SInE strategy applied
% 0.13/0.26 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.13/0.26 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.26 % Starting SubtermCWHack with 151s (1) cores
% 0.13/0.26 % Starting pre_casc_2 with 901s (1) cores
% 0.13/0.26 % Starting sh2 with 151s (1) cores
% 0.13/0.26 % Preprocessing time : 0.002 s
% 0.13/0.26 % Presaturation interreduction done
% 0.13/0.26
% 0.13/0.26 % Proof found!
% 0.13/0.26 % SZS status Theorem
% 0.13/0.26 % SZS output start CNFRefutation
% See solution above
% 0.13/0.26 % Parsed axioms : 29
% 0.13/0.26 % Removed by relevancy pruning/SinE : 0
% 0.13/0.26 % Initial clauses : 29
% 0.13/0.26 % Removed in clause preprocessing : 14
% 0.13/0.26 % Initial clauses in saturation : 15
% 0.13/0.26 % Processed clauses : 32
% 0.13/0.26 % ...of these trivial : 3
% 0.13/0.26 % ...subsumed : 0
% 0.13/0.26 % ...remaining for further processing : 29
% 0.13/0.26 % Other redundant clauses eliminated : 0
% 0.13/0.26 % Clauses deleted for lack of memory : 0
% 0.13/0.26 % Backward-subsumed : 0
% 0.13/0.26 % Backward-rewritten : 2
% 0.13/0.26 % Generated clauses : 56
% 0.13/0.26 % ...of the previous two non-redundant : 51
% 0.13/0.26 % ...aggressively subsumed : 0
% 0.13/0.26 % Contextual simplify-reflections : 0
% 0.13/0.26 % Paramodulations : 50
% 0.13/0.26 % Factorizations : 0
% 0.13/0.26 % NegExts : 3
% 0.13/0.26 % Equation resolutions : 0
% 0.13/0.26 % Disequality decompositions : 0
% 0.13/0.26 % Total rewrite steps : 100
% 0.13/0.26 % ...of those cached : 77
% 0.13/0.26 % Propositional unsat checks : 0
% 0.13/0.26 % Propositional check models : 0
% 0.13/0.26 % Propositional check unsatisfiable : 0
% 0.13/0.26 % Propositional clauses : 0
% 0.13/0.26 % Propositional clauses after purity: 0
% 0.13/0.26 % Propositional unsat core size : 0
% 0.13/0.26 % Propositional preprocessing time : 0.000
% 0.13/0.26 % Propositional encoding time : 0.000
% 0.13/0.26 % Propositional solver time : 0.000
% 0.13/0.26 % Success case prop preproc time : 0.000
% 0.13/0.26 % Success case prop encoding time : 0.000
% 0.13/0.26 % Success case prop solver time : 0.000
% 0.13/0.26 % Current number of processed clauses : 12
% 0.13/0.26 % Positive orientable unit clauses : 8
% 0.13/0.26 % Positive unorientable unit clauses: 1
% 0.13/0.26 % Negative unit clauses : 3
% 0.13/0.26 % Non-unit-clauses : 0
% 0.13/0.26 % Current number of unprocessed clauses: 48
% 0.13/0.26 % ...number of literals in the above : 48
% 0.13/0.26 % Current number of archived formulas : 0
% 0.13/0.26 % Current number of archived clauses : 17
% 0.13/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.13/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.13/0.26 % Non-unit clause-clause subsumptions : 0
% 0.13/0.26 % Unit Clause-clause subsumption calls : 8
% 0.13/0.26 % Rewrite failures with RHS unbound : 0
% 0.13/0.26 % BW rewrite match attempts : 248
% 0.13/0.26 % BW rewrite match successes : 4
% 0.13/0.26 % Condensation attempts : 0
% 0.13/0.26 % Condensation successes : 0
% 0.13/0.26 % Termbank termtop insertions : 2424
% 0.13/0.26 % Search garbage collected termcells : 87
% 0.13/0.26
% 0.13/0.26 % -------------------------------------------------
% 0.13/0.26 % User time : 0.007 s
% 0.13/0.26 % System time : 0.004 s
% 0.13/0.26 % Total time : 0.011 s
% 0.13/0.26 % Maximum resident set size: 3596 pages
% 0.13/0.26
% 0.13/0.26 % -------------------------------------------------
% 0.13/0.26 % User time : 0.038 s
% 0.13/0.26 % System time : 0.014 s
% 0.13/0.26 % Total time : 0.052 s
% 0.13/0.26 % Maximum resident set size: 4864 pages
% 0.13/0.26 % E exiting
%------------------------------------------------------------------------------