%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM021^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 3.63s 0.86s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 37 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 174 ( 10 ~; 4 |; 2 &; 158 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 63 ( 12 ^; 49 !; 2 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
one: ( $i > $i ) > $i > $i ).
thf(decl_25,type,
two: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_28,type,
five: ( $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 ) > $i > $i ) > ( $i > $i ) > $i > $i ) > $i > $i ).
thf(decl_41,type,
esk5_1: ( ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ) > $i ).
thf(thm,conjecture,
? [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ two @ three )
= five )
& ( ( X5 @ one @ two )
= three ) ),
file('/export/starexec/sandbox/tmp/tmp.PyK6otC2HG/E---3.1_613697.p',thm) ).
thf(two_ax,axiom,
( two
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PyK6otC2HG/E---3.1_613697.p',two_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PyK6otC2HG/E---3.1_613697.p',one_ax) ).
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/sandbox/tmp/tmp.PyK6otC2HG/E---3.1_613697.p',plus_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PyK6otC2HG/E---3.1_613697.p',three_ax) ).
thf(five_ax,axiom,
( five
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PyK6otC2HG/E---3.1_613697.p',five_ax) ).
thf(c_0_6,negated_conjecture,
~ ? [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ two @ three )
= five )
& ( ( X5 @ one @ two )
= three ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,plain,
! [X11: $i > $i,X12: $i] :
( ( two @ X11 @ X12 )
= ( X11 @ ( X11 @ X12 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).
thf(c_0_8,negated_conjecture,
! [X73: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X73 @ two @ three )
!= five )
| ( ( X73 @ one @ two )
!= three ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_9,plain,
! [X9: $i > $i,X10: $i] :
( ( one @ X9 @ X10 )
= ( X9 @ X10 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[one_ax])]) ).
thf(c_0_10,plain,
! [X32: ( $i > $i ) > $i > $i,X33: ( $i > $i ) > $i > $i,X34: $i > $i,X35: $i] :
( ( plus @ X32 @ X33 @ X34 @ X35 )
= ( X32 @ X34 @ ( X33 @ X34 @ X35 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[plus_ax])]) ).
thf(c_0_11,plain,
! [X44: $i > $i,X45: $i] :
( ( two @ X44 @ X45 )
= ( X44 @ ( X44 @ X45 ) ) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X13: $i > $i,X14: $i] :
( ( three @ X13 @ X14 )
= ( X13 @ ( X13 @ ( X13 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).
thf(c_0_13,negated_conjecture,
! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ two @ three )
!= five )
| ( ( X5 @ one @ two )
!= three ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
! [X42: $i > $i,X43: $i] :
( ( one @ X42 @ X43 )
= ( X42 @ X43 ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
! [X65: ( $i > $i ) > $i > $i,X66: ( $i > $i ) > $i > $i,X67: $i > $i,X68: $i] :
( ( plus @ X65 @ X66 @ X67 @ X68 )
= ( X65 @ X67 @ ( X66 @ X67 @ X68 ) ) ),
inference(variable_rename,[status(thm)],[c_0_10]) ).
thf(c_0_16,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ X2 )
= ( X1 @ ( X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X46: $i > $i,X47: $i] :
( ( three @ X46 @ X47 )
= ( X46 @ ( X46 @ ( X46 @ X47 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
! [X17: $i > $i,X18: $i] :
( ( five @ X17 @ X18 )
= ( X17 @ ( X17 @ ( X17 @ ( X17 @ ( X17 @ X18 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[five_ax])]) ).
thf(c_0_19,negated_conjecture,
! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ one @ two @ ( esk1_2 @ X5 ) )
!= ( three @ ( esk1_2 @ X5 ) ) )
| ( ( X5 @ two @ three )
!= five ) ),
inference(neg_ext,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,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_15]) ).
thf(c_0_22,plain,
! [X1: $i > $i,X2: $i] :
( ( two @ X1 @ ( X1 @ X2 ) )
= ( X1 @ ( two @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
thf(c_0_23,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,plain,
! [X50: $i > $i,X51: $i] :
( ( five @ X50 @ X51 )
= ( X50 @ ( X50 @ ( X50 @ ( X50 @ ( X50 @ X51 ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_18]) ).
thf(c_0_25,negated_conjecture,
! [X5: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i] :
( ( ( X5 @ one @ two @ ( esk1_2 @ X5 ) @ ( esk5_1 @ X5 ) )
!= ( three @ ( esk1_2 @ X5 ) @ ( esk5_1 @ X5 ) ) )
| ( ( X5 @ two @ three )
!= five ) ),
inference(neg_ext,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( plus @ one @ X3 @ X1 @ X2 )
= ( X1 @ ( X3 @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
thf(c_0_27,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( two @ X1 @ X2 ) )
= ( three @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_22]),c_0_23]) ).
thf(c_0_28,plain,
! [X1: $i > $i,X2: $i] :
( ( five @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
thf(c_0_29,negated_conjecture,
( ( plus @ two @ three )
!= five ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
thf(c_0_30,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( X1 @ ( three @ X1 @ X2 ) ) )
= ( five @ X1 @ X2 ) ),
inference(rw,[status(thm)],[c_0_28,c_0_23]) ).
thf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(neg_ext,[status(thm)],[c_0_29]),c_0_21]),c_0_16]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM021^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 11:52:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.PyK6otC2HG/E---3.1_613697.p
% 3.63/0.86 % Version: 3.5.1-ho
% 3.63/0.86 % Preprocessing class: HSSSSMSSMSSNHHA.
% 3.63/0.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.63/0.86 % Starting new_ho_10 with 1500s (5) cores
% 3.63/0.86 % Starting ho_unfolding_6 with 300s (1) cores
% 3.63/0.86 % Starting sh4l with 300s (1) cores
% 3.63/0.86 % Starting ehoh_best_nonlift with 300s (1) cores
% 3.63/0.86 % new_ho_10 with pid 613710 completed with status 0
% 3.63/0.86 % Result found by new_ho_10
% 3.63/0.86 % Preprocessing class: HSSSSMSSMSSNHHA.
% 3.63/0.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.63/0.86 % Starting new_ho_10 with 1500s (5) cores
% 3.63/0.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.63/0.86 % No SInE strategy applied
% 3.63/0.86 % Search class: HUHPM-FFSF32-DHHSFMNN
% 3.63/0.86 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 3.63/0.86 % Starting SubtermCWHack with 151s (1) cores
% 3.63/0.86 % Starting new_ho_10 with 901s (1) cores
% 3.63/0.86 % Starting ho_unfolding_6 with 151s (1) cores
% 3.63/0.86 % Starting sh4l with 151s (1) cores
% 3.63/0.86 % Starting ehoh_best_nonlift with 146s (1) cores
% 3.63/0.86 % new_ho_10 with pid 613715 completed with status 0
% 3.63/0.86 % Result found by new_ho_10
% 3.63/0.86 % Preprocessing class: HSSSSMSSMSSNHHA.
% 3.63/0.86 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.63/0.86 % Starting new_ho_10 with 1500s (5) cores
% 3.63/0.86 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.63/0.86 % No SInE strategy applied
% 3.63/0.86 % Search class: HUHPM-FFSF32-DHHSFMNN
% 3.63/0.86 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 3.63/0.86 % Starting SubtermCWHack with 151s (1) cores
% 3.63/0.86 % Starting new_ho_10 with 901s (1) cores
% 3.63/0.86 % Preprocessing time : 0.001 s
% 3.63/0.86 % Presaturation interreduction done
% 3.63/0.86
% 3.63/0.86 % Proof found!
% 3.63/0.86 % SZS status Theorem
% 3.63/0.86 % SZS output start CNFRefutation
% See solution above
% 3.63/0.87 % Parsed axioms : 29
% 3.63/0.87 % Removed by relevancy pruning/SinE : 0
% 3.63/0.87 % Initial clauses : 29
% 3.63/0.87 % Removed in clause preprocessing : 14
% 3.63/0.87 % Initial clauses in saturation : 15
% 3.63/0.87 % Processed clauses : 479
% 3.63/0.87 % ...of these trivial : 108
% 3.63/0.87 % ...subsumed : 16
% 3.63/0.87 % ...remaining for further processing : 354
% 3.63/0.87 % Other redundant clauses eliminated : 0
% 3.63/0.87 % Clauses deleted for lack of memory : 0
% 3.63/0.87 % Backward-subsumed : 0
% 3.63/0.87 % Backward-rewritten : 75
% 3.63/0.87 % Generated clauses : 13221
% 3.63/0.87 % ...of the previous two non-redundant : 11416
% 3.63/0.87 % ...aggressively subsumed : 0
% 3.63/0.87 % Contextual simplify-reflections : 0
% 3.63/0.87 % Paramodulations : 13032
% 3.63/0.87 % Factorizations : 0
% 3.63/0.87 % NegExts : 91
% 3.63/0.87 % Equation resolutions : 0
% 3.63/0.87 % Disequality decompositions : 0
% 3.63/0.87 % Total rewrite steps : 23905
% 3.63/0.87 % ...of those cached : 19507
% 3.63/0.87 % Propositional unsat checks : 0
% 3.63/0.87 % Propositional check models : 0
% 3.63/0.87 % Propositional check unsatisfiable : 0
% 3.63/0.87 % Propositional clauses : 0
% 3.63/0.87 % Propositional clauses after purity: 0
% 3.63/0.87 % Propositional unsat core size : 0
% 3.63/0.87 % Propositional preprocessing time : 0.000
% 3.63/0.87 % Propositional encoding time : 0.000
% 3.63/0.87 % Propositional solver time : 0.000
% 3.63/0.87 % Success case prop preproc time : 0.000
% 3.63/0.87 % Success case prop encoding time : 0.000
% 3.63/0.87 % Success case prop solver time : 0.000
% 3.63/0.87 % Current number of processed clauses : 264
% 3.63/0.87 % Positive orientable unit clauses : 126
% 3.63/0.87 % Positive unorientable unit clauses: 15
% 3.63/0.87 % Negative unit clauses : 6
% 3.63/0.87 % Non-unit-clauses : 117
% 3.63/0.87 % Current number of unprocessed clauses: 10761
% 3.63/0.87 % ...number of literals in the above : 10761
% 3.63/0.87 % Current number of archived formulas : 0
% 3.63/0.87 % Current number of archived clauses : 90
% 3.63/0.87 % Clause-clause subsumption calls (NU) : 10171
% 3.63/0.87 % Rec. Clause-clause subsumption calls : 6079
% 3.63/0.87 % Non-unit clause-clause subsumptions : 0
% 3.63/0.87 % Unit Clause-clause subsumption calls : 658
% 3.63/0.87 % Rewrite failures with RHS unbound : 0
% 3.63/0.87 % BW rewrite match attempts : 29033
% 3.63/0.87 % BW rewrite match successes : 96
% 3.63/0.87 % Condensation attempts : 479
% 3.63/0.87 % Condensation successes : 0
% 3.63/0.87 % Termbank termtop insertions : 717215
% 3.63/0.87 % Search garbage collected termcells : 98
% 3.63/0.87
% 3.63/0.87 % -------------------------------------------------
% 3.63/0.87 % User time : 0.559 s
% 3.63/0.87 % System time : 0.017 s
% 3.63/0.87 % Total time : 0.577 s
% 3.63/0.87 % Maximum resident set size: 3652 pages
% 3.63/0.87
% 3.63/0.87 % -------------------------------------------------
% 3.63/0.87 % User time : 2.328 s
% 3.63/0.87 % System time : 0.118 s
% 3.63/0.87 % Total time : 2.445 s
% 3.63/0.87 % Maximum resident set size: 4864 pages
% 3.63/0.87 % E exiting
%------------------------------------------------------------------------------