%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM020^1 : 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 : n006.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 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 33 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 175 ( 4 ~; 0 |; 0 &; 171 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 1 con; 0-4 aty)
% Number of variables : 69 ( 14 ^; 53 !; 2 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
two: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_27,type,
four: ( $i > $i ) > $i > $i ).
thf(decl_28,type,
five: ( $i > $i ) > $i > $i ).
thf(decl_29,type,
six: ( $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_38,type,
esk2_1: ( ( $i > $i ) > $i > $i ) > $i ).
thf(four_ax,axiom,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.p',four_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.p',three_ax) ).
thf(five_ax,axiom,
( five
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.p',five_ax) ).
thf(six_ax,axiom,
( six
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.p',six_ax) ).
thf(thm,conjecture,
? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three )
= six ),
file('/export/starexec/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.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/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.p',mult_ax) ).
thf(two_ax,axiom,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LqrrIMxVFU/E---3.1_617568.p',two_ax) ).
thf(c_0_7,plain,
! [X14: $i > $i,X15: $i] :
( ( four @ X14 @ X15 )
= ( X14 @ ( X14 @ ( X14 @ ( X14 @ X15 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[four_ax])]) ).
thf(c_0_8,plain,
! [X12: $i > $i,X13: $i] :
( ( three @ X12 @ X13 )
= ( X12 @ ( X12 @ ( X12 @ X13 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_9,plain,
! [X16: $i > $i,X17: $i] :
( ( five @ X16 @ X17 )
= ( X16 @ ( X16 @ ( X16 @ ( X16 @ ( X16 @ X17 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[five_ax])]) ).
thf(c_0_10,plain,
! [X47: $i > $i,X48: $i] :
( ( four @ X47 @ X48 )
= ( X47 @ ( X47 @ ( X47 @ ( X47 @ X48 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X45: $i > $i,X46: $i] :
( ( three @ X45 @ X46 )
= ( X45 @ ( X45 @ ( X45 @ X46 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X18: $i > $i,X19: $i] :
( ( six @ X18 @ X19 )
= ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ X19 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).
thf(c_0_13,plain,
! [X49: $i > $i,X50: $i] :
( ( five @ X49 @ X50 )
= ( X49 @ ( X49 @ ( X49 @ ( X49 @ ( X49 @ X50 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: $i > $i,X2: $i] :
( ( four @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three )
= six ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_17,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_18,plain,
! [X51: $i > $i,X52: $i] :
( ( six @ X51 @ X52 )
= ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ X52 ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( three @ X1 @ X2 ) )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_21,plain,
! [X10: $i > $i,X11: $i] :
( ( two @ X10 @ X11 )
= ( X10 @ ( X10 @ X11 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_22,negated_conjecture,
! [X72: ( $i > $i ) > $i > $i] :
( ( mult @ X72 @ three )
!= six ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
thf(c_0_23,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_17]) ).
thf(c_0_24,plain,
! [X1: $i > $i,X2: $i] :
( ( six @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_25,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( four @ X1 @ X2 ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_15]),c_0_20]) ).
thf(c_0_26,plain,
! [X43: $i > $i,X44: $i] :
( ( two @ X43 @ X44 )
= ( X43 @ ( X43 @ X44 ) ) ),
inference(variable_rename,[status(thm)],[c_0_21]) ).
thf(c_0_27,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( mult @ X3 @ three )
!= six ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_28,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_23]) ).
thf(c_0_29,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( five @ X1 @ X2 ) )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_15]),c_0_20]),c_0_25]) ).
thf(c_0_30,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( three @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) )
!= ( six @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_27]),c_0_28]) ).
thf(c_0_32,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ ( three @ X1 ) @ X2 )
= ( six @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_25]),c_0_29]),c_0_30]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 11:55:24 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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.LqrrIMxVFU/E---3.1_617568.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting pre_casc_2 with 1500s (5) cores
% 0.21/0.29 % Starting sh2 with 300s (1) cores
% 0.21/0.29 % Starting sh3 with 300s (1) cores
% 0.21/0.29 % Starting new_ho_10 with 300s (1) cores
% 0.21/0.29 % pre_casc_2 with pid 617597 completed with status 0
% 0.21/0.29 % Result found by pre_casc_2
% 0.21/0.29 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting pre_casc_2 with 1500s (5) cores
% 0.21/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.21/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.29 % Starting pre_casc_2 with 901s (1) cores
% 0.21/0.29 % Starting sh2 with 151s (1) cores
% 0.21/0.29 % Starting sh3 with 151s (1) cores
% 0.21/0.29 % Starting sh9 with 146s (1) cores
% 0.21/0.29 % sh9 with pid 617610 completed with status 0
% 0.21/0.29 % Result found by sh9
% 0.21/0.29 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting pre_casc_2 with 1500s (5) cores
% 0.21/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.21/0.29 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.29 % Starting SubtermCWHack with 151s (1) cores
% 0.21/0.29 % Starting pre_casc_2 with 901s (1) cores
% 0.21/0.29 % Starting sh2 with 151s (1) cores
% 0.21/0.29 % Starting sh3 with 151s (1) cores
% 0.21/0.29 % Starting sh9 with 146s (1) cores
% 0.21/0.29 % Preprocessing time : 0.001 s
% 0.21/0.29 % Presaturation interreduction done
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% See solution above
% 0.21/0.29 % Parsed axioms : 29
% 0.21/0.29 % Removed by relevancy pruning/SinE : 0
% 0.21/0.29 % Initial clauses : 29
% 0.21/0.29 % Removed in clause preprocessing : 14
% 0.21/0.29 % Initial clauses in saturation : 15
% 0.21/0.29 % Processed clauses : 78
% 0.21/0.29 % ...of these trivial : 14
% 0.21/0.29 % ...subsumed : 0
% 0.21/0.29 % ...remaining for further processing : 64
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 0
% 0.21/0.29 % Backward-rewritten : 1
% 0.21/0.29 % Generated clauses : 655
% 0.21/0.29 % ...of the previous two non-redundant : 633
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 648
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 3
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 397
% 0.21/0.29 % ...of those cached : 349
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 48
% 0.21/0.29 % Positive orientable unit clauses : 31
% 0.21/0.29 % Positive unorientable unit clauses: 3
% 0.21/0.29 % Negative unit clauses : 14
% 0.21/0.29 % Non-unit-clauses : 0
% 0.21/0.29 % Current number of unprocessed clauses: 566
% 0.21/0.29 % ...number of literals in the above : 566
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 16
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.29 % Non-unit clause-clause subsumptions : 0
% 0.21/0.29 % Unit Clause-clause subsumption calls : 43
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 666
% 0.21/0.29 % BW rewrite match successes : 7
% 0.21/0.29 % Condensation attempts : 78
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 15758
% 0.21/0.29 % Search garbage collected termcells : 87
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.018 s
% 0.21/0.29 % System time : 0.005 s
% 0.21/0.29 % Total time : 0.023 s
% 0.21/0.29 % Maximum resident set size: 3648 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.115 s
% 0.21/0.29 % System time : 0.020 s
% 0.21/0.29 % Total time : 0.135 s
% 0.21/0.29 % Maximum resident set size: 4864 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------