%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM419^1 : 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 : n003.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 08:16:38 AM UTC 2026
% Result : Theorem 0.35s 0.45s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 143 ( 5 ~; 0 |; 0 &; 138 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 62 ( 13 ^; 47 !; 2 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
one: ( $i > $i ) > $i > $i ).
thf(decl_26,type,
three: ( $i > $i ) > $i > $i ).
thf(decl_27,type,
four: ( $i > $i ) > $i > $i ).
thf(decl_34,type,
succ: ( ( $i > $i ) > $i > $i ) > ( $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 )
= four ),
file('/export/starexec/sandbox/tmp/tmp.JbbdN2Aa6V/E---3.1_2426538.p',thm) ).
thf(succ_ax,axiom,
( succ
= ( ^ [X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X3 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbbdN2Aa6V/E---3.1_2426538.p',succ_ax) ).
thf(three_ax,axiom,
( three
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbbdN2Aa6V/E---3.1_2426538.p',three_ax) ).
thf(four_ax,axiom,
( four
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbbdN2Aa6V/E---3.1_2426538.p',four_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.JbbdN2Aa6V/E---3.1_2426538.p',plus_ax) ).
thf(one_ax,axiom,
( one
= ( ^ [X1: $i > $i,X2: $i] : ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.JbbdN2Aa6V/E---3.1_2426538.p',one_ax) ).
thf(c_0_6,negated_conjecture,
~ ? [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three )
= four ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,plain,
! [X28: ( $i > $i ) > $i > $i,X29: $i > $i,X30: $i] :
( ( succ @ X28 @ X29 @ X30 )
= ( X29 @ ( X28 @ X29 @ X30 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[succ_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,
! [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_10,negated_conjecture,
! [X72: ( $i > $i ) > $i > $i] :
( ( plus @ X72 @ three )
!= four ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_11,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_12,plain,
! [X61: ( $i > $i ) > $i > $i,X62: $i > $i,X63: $i] :
( ( succ @ X61 @ X62 @ X63 )
= ( X62 @ ( X61 @ X62 @ X63 ) ) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
thf(c_0_13,plain,
! [X45: $i > $i,X46: $i] :
( ( three @ X45 @ X46 )
= ( X45 @ ( X45 @ ( X45 @ X46 ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
! [X47: $i > $i,X48: $i] :
( ( four @ X47 @ X48 )
= ( X47 @ ( X47 @ ( X47 @ ( X47 @ X48 ) ) ) ) ),
inference(variable_rename,[status(thm)],[c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three )
!= four ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,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_11]) ).
thf(c_0_17,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_18,plain,
! [X1: $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
( ( succ @ X3 @ X1 @ X2 )
= ( X1 @ ( X3 @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,plain,
! [X1: $i > $i,X2: $i] :
( ( three @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_20,plain,
! [X1: $i > $i,X2: $i] :
( ( four @ X1 @ X2 )
= ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_21,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( plus @ X3 @ three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) )
!= ( four @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(neg_ext,[status(thm)],[c_0_15]) ).
thf(c_0_22,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_16]) ).
thf(c_0_23,plain,
! [X41: $i > $i,X42: $i] :
( ( one @ X41 @ X42 )
= ( X41 @ X42 ) ),
inference(variable_rename,[status(thm)],[c_0_17]) ).
thf(c_0_24,plain,
! [X1: $i > $i,X2: $i] :
( ( succ @ three @ X1 @ X2 )
= ( four @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
thf(c_0_25,negated_conjecture,
! [X3: ( $i > $i ) > $i > $i] :
( ( X3 @ ( esk1_2 @ X3 ) @ ( three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) )
!= ( four @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_26,plain,
! [X1: $i > $i,X2: $i] :
( ( one @ X1 @ X2 )
= ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ ( three @ X1 @ X2 ) )
= ( four @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM419^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n003.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Tue Sep 29 12:04:43 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.34 Running higher-order theorem proving
% 0.27/0.36 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.JbbdN2Aa6V/E---3.1_2426538.p
% 0.35/0.45 % Version: 3.5.1-ho
% 0.35/0.45 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.35/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.45 % Starting pre_casc_2 with 1500s (5) cores
% 0.35/0.45 % Starting sh2 with 300s (1) cores
% 0.35/0.45 % Starting sh3 with 300s (1) cores
% 0.35/0.45 % Starting new_ho_10 with 300s (1) cores
% 0.35/0.45 % pre_casc_2 with pid 2426551 completed with status 0
% 0.35/0.45 % Result found by pre_casc_2
% 0.35/0.45 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.35/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.45 % Starting pre_casc_2 with 1500s (5) cores
% 0.35/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.35/0.45 % No SInE strategy applied
% 0.35/0.45 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.35/0.45 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.35/0.45 % Starting SubtermCWHack with 151s (1) cores
% 0.35/0.45 % Starting pre_casc_2 with 901s (1) cores
% 0.35/0.45 % Starting sh2 with 151s (1) cores
% 0.35/0.45 % Starting sh3 with 151s (1) cores
% 0.35/0.45 % Starting sh9 with 146s (1) cores
% 0.35/0.45 % pre_casc_2 with pid 2426558 completed with status 0
% 0.35/0.45 % Result found by pre_casc_2
% 0.35/0.45 % Preprocessing class: HSSSSMSSMSSNHHN.
% 0.35/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.45 % Starting pre_casc_2 with 1500s (5) cores
% 0.35/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.35/0.45 % No SInE strategy applied
% 0.35/0.45 % Search class: HUUPM-FFSF32-DHHSFMNN
% 0.35/0.45 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.35/0.45 % Starting SubtermCWHack with 151s (1) cores
% 0.35/0.45 % Starting pre_casc_2 with 901s (1) cores
% 0.35/0.45 % Preprocessing time : 0.002 s
% 0.35/0.45 % Presaturation interreduction done
% 0.35/0.45
% 0.35/0.45 % Proof found!
% 0.35/0.45 % SZS status Theorem
% 0.35/0.45 % SZS output start CNFRefutation
% See solution above
% 0.35/0.45 % Parsed axioms : 29
% 0.35/0.45 % Removed by relevancy pruning/SinE : 0
% 0.35/0.45 % Initial clauses : 29
% 0.35/0.45 % Removed in clause preprocessing : 14
% 0.35/0.45 % Initial clauses in saturation : 15
% 0.35/0.45 % Processed clauses : 151
% 0.35/0.45 % ...of these trivial : 55
% 0.35/0.45 % ...subsumed : 5
% 0.35/0.45 % ...remaining for further processing : 90
% 0.35/0.45 % Other redundant clauses eliminated : 0
% 0.35/0.45 % Clauses deleted for lack of memory : 0
% 0.35/0.45 % Backward-subsumed : 0
% 0.35/0.45 % Backward-rewritten : 0
% 0.35/0.45 % Generated clauses : 1577
% 0.35/0.45 % ...of the previous two non-redundant : 1486
% 0.35/0.45 % ...aggressively subsumed : 0
% 0.35/0.45 % Contextual simplify-reflections : 0
% 0.35/0.45 % Paramodulations : 1538
% 0.35/0.45 % Factorizations : 0
% 0.35/0.45 % NegExts : 3
% 0.35/0.45 % Equation resolutions : 0
% 0.35/0.45 % Disequality decompositions : 0
% 0.35/0.45 % Total rewrite steps : 1374
% 0.35/0.45 % ...of those cached : 1176
% 0.35/0.45 % Propositional unsat checks : 0
% 0.35/0.45 % Propositional check models : 0
% 0.35/0.45 % Propositional check unsatisfiable : 0
% 0.35/0.45 % Propositional clauses : 0
% 0.35/0.45 % Propositional clauses after purity: 0
% 0.35/0.45 % Propositional unsat core size : 0
% 0.35/0.45 % Propositional preprocessing time : 0.000
% 0.35/0.45 % Propositional encoding time : 0.000
% 0.35/0.45 % Propositional solver time : 0.000
% 0.35/0.45 % Success case prop preproc time : 0.000
% 0.35/0.45 % Success case prop encoding time : 0.000
% 0.35/0.45 % Success case prop solver time : 0.000
% 0.35/0.45 % Current number of processed clauses : 75
% 0.35/0.45 % Positive orientable unit clauses : 57
% 0.35/0.45 % Positive unorientable unit clauses: 8
% 0.35/0.45 % Negative unit clauses : 10
% 0.35/0.45 % Non-unit-clauses : 0
% 0.35/0.45 % Current number of unprocessed clauses: 1365
% 0.35/0.45 % ...number of literals in the above : 1365
% 0.35/0.45 % Current number of archived formulas : 0
% 0.35/0.45 % Current number of archived clauses : 15
% 0.35/0.45 % Clause-clause subsumption calls (NU) : 0
% 0.35/0.45 % Rec. Clause-clause subsumption calls : 0
% 0.35/0.45 % Non-unit clause-clause subsumptions : 0
% 0.35/0.45 % Unit Clause-clause subsumption calls : 47
% 0.35/0.45 % Rewrite failures with RHS unbound : 0
% 0.35/0.45 % BW rewrite match attempts : 992
% 0.35/0.45 % BW rewrite match successes : 5
% 0.35/0.45 % Condensation attempts : 151
% 0.35/0.45 % Condensation successes : 0
% 0.35/0.45 % Termbank termtop insertions : 35472
% 0.35/0.45 % Search garbage collected termcells : 87
% 0.35/0.45
% 0.35/0.45 % -------------------------------------------------
% 0.35/0.45 % User time : 0.054 s
% 0.35/0.45 % System time : 0.005 s
% 0.35/0.45 % Total time : 0.059 s
% 0.35/0.45 % Maximum resident set size: 3648 pages
% 0.35/0.45
% 0.35/0.45 % -------------------------------------------------
% 0.35/0.45 % User time : 0.232 s
% 0.35/0.45 % System time : 0.032 s
% 0.35/0.45 % Total time : 0.264 s
% 0.35/0.45 % Maximum resident set size: 4864 pages
% 0.35/0.45 % E exiting
%------------------------------------------------------------------------------