%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:05:40 AM UTC 2026
% Result : Theorem 0.79s 0.43s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 23 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 16 ~; 8 |; 0 &; 42 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 20 !; 2 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
polyno727731844poly_a: $tType ).
thf(decl_26,type,
zero_zero_nat: nat ).
thf(decl_27,type,
suc: nat > nat ).
thf(decl_31,type,
ord_less_nat: nat > nat > $o ).
thf(decl_34,type,
polyno578545843gree_a: polyno727731844poly_a > nat ).
thf(decl_37,type,
polyno1372495879olyh_a: polyno727731844poly_a > nat > $o ).
thf(decl_40,type,
n: nat ).
thf(decl_41,type,
p: polyno727731844poly_a ).
thf(decl_54,type,
esk13_1: nat > nat ).
thf(fact_69_not0__implies__Suc,axiom,
! [X1: nat] :
( ( X1 != zero_zero_nat )
=> ? [X29: nat] :
( X1
= ( suc @ X29 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gSjEbEBW3q/E---3.1_574161.p',fact_69_not0__implies__Suc) ).
thf(conj_2,conjecture,
( ( polyno578545843gree_a @ p )
= zero_zero_nat ),
file('/export/starexec/sandbox2/tmp/tmp.gSjEbEBW3q/E---3.1_574161.p',conj_2) ).
thf(fact_8_gr__implies__not0,axiom,
! [X3: nat,X1: nat] :
( ( ord_less_nat @ X3 @ X1 )
=> ( X1 != zero_zero_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.gSjEbEBW3q/E---3.1_574161.p',fact_8_gr__implies__not0) ).
thf(fact_31_degree__isnpolyh__Suc,axiom,
! [X13: polyno727731844poly_a,X1: nat] :
( ( polyno1372495879olyh_a @ X13 @ ( suc @ X1 ) )
=> ( ( polyno578545843gree_a @ X13 )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/tmp/tmp.gSjEbEBW3q/E---3.1_574161.p',fact_31_degree__isnpolyh__Suc) ).
thf(conj_0,hypothesis,
ord_less_nat @ zero_zero_nat @ n,
file('/export/starexec/sandbox2/tmp/tmp.gSjEbEBW3q/E---3.1_574161.p',conj_0) ).
thf(conj_1,hypothesis,
polyno1372495879olyh_a @ p @ n,
file('/export/starexec/sandbox2/tmp/tmp.gSjEbEBW3q/E---3.1_574161.p',conj_1) ).
thf(c_0_6,plain,
! [X1: nat] :
( ( X1 != zero_zero_nat )
=> ? [X29: nat] :
( X1
= ( suc @ X29 ) ) ),
inference(fof_simplification,[status(thm)],[fact_69_not0__implies__Suc]) ).
thf(c_0_7,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(assume_negation,[status(cth)],[conj_2]) ).
thf(c_0_8,plain,
! [X3: nat,X1: nat] :
( ( ord_less_nat @ X3 @ X1 )
=> ( X1 != zero_zero_nat ) ),
inference(fof_simplification,[status(thm)],[fact_8_gr__implies__not0]) ).
thf(c_0_9,plain,
! [X1311: polyno727731844poly_a,X1312: nat] :
( ~ ( polyno1372495879olyh_a @ X1311 @ ( suc @ X1312 ) )
| ( ( polyno578545843gree_a @ X1311 )
= zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_31_degree__isnpolyh__Suc])])]) ).
thf(c_0_10,plain,
! [X1373: nat] :
( ( X1373 = zero_zero_nat )
| ( X1373
= ( suc @ ( esk13_1 @ X1373 ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_11,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
thf(c_0_12,plain,
! [X1273: nat,X1274: nat] :
( ~ ( ord_less_nat @ X1273 @ X1274 )
| ( X1274 != zero_zero_nat ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_13,plain,
! [X12: polyno727731844poly_a,X1: nat] :
( ( ( polyno578545843gree_a @ X12 )
= zero_zero_nat )
| ~ ( polyno1372495879olyh_a @ X12 @ ( suc @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: nat] :
( ( X1 = zero_zero_nat )
| ( X1
= ( suc @ ( esk13_1 @ X1 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(fof_nnf,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: nat,X2: nat] :
( ~ ( ord_less_nat @ X1 @ X2 )
| ( X2 != zero_zero_nat ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,hypothesis,
ord_less_nat @ zero_zero_nat @ n,
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_18,plain,
! [X12: polyno727731844poly_a,X1: nat] :
( ( ( polyno578545843gree_a @ X12 )
= zero_zero_nat )
| ( X1 = zero_zero_nat )
| ~ ( polyno1372495879olyh_a @ X12 @ X1 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_19,hypothesis,
polyno1372495879olyh_a @ p @ n,
inference(split_conjunct,[status(thm)],[conj_1]) ).
thf(c_0_20,negated_conjecture,
( ( polyno578545843gree_a @ p )
!= zero_zero_nat ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_21,hypothesis,
n != zero_zero_nat,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_22,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP151^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.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 20:04:26 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.gSjEbEBW3q/E---3.1_574161.p
% 0.79/0.43 % Version: 3.5.1-ho
% 0.79/0.43 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.79/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.79/0.43 % Starting new_ho_10_unif with 300s (1) cores
% 0.79/0.43 % Starting sh10 with 300s (1) cores
% 0.79/0.43 % Starting lpo5_rw_fix with 300s (1) cores
% 0.79/0.43 % new_ho_10 with pid 574174 completed with status 0
% 0.79/0.43 % Result found by new_ho_10
% 0.79/0.43 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.79/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.79/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.79/0.43 % No SInE strategy applied
% 0.79/0.43 % Search class: HGHSM-FSLM32-MHFFFSBC
% 0.79/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.79/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.79/0.43 % Starting new_ho_10 with 151s (1) cores
% 0.79/0.43 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.79/0.43 % Starting new_ho_3 with 136s (1) cores
% 0.79/0.43 % Starting sh3 with 136s (1) cores
% 0.79/0.43 % lpo6_lambda_fix with pid 574183 completed with status 0
% 0.79/0.43 % Result found by lpo6_lambda_fix
% 0.79/0.43 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.79/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.43 % Starting new_ho_10 with 1500s (5) cores
% 0.79/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.79/0.43 % No SInE strategy applied
% 0.79/0.43 % Search class: HGHSM-FSLM32-MHFFFSBC
% 0.79/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.79/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.79/0.43 % Starting new_ho_10 with 151s (1) cores
% 0.79/0.43 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.79/0.43 % Preprocessing time : 0.007 s
% 0.79/0.43
% 0.79/0.43 % Proof found!
% 0.79/0.43 % SZS status Theorem
% 0.79/0.43 % SZS output start CNFRefutation
% See solution above
% 0.79/0.43 % Parsed axioms : 373
% 0.79/0.43 % Removed by relevancy pruning/SinE : 0
% 0.79/0.43 % Initial clauses : 712
% 0.79/0.43 % Removed in clause preprocessing : 47
% 0.79/0.43 % Initial clauses in saturation : 665
% 0.79/0.43 % Processed clauses : 834
% 0.79/0.43 % ...of these trivial : 15
% 0.79/0.43 % ...subsumed : 394
% 0.79/0.43 % ...remaining for further processing : 425
% 0.79/0.43 % Other redundant clauses eliminated : 81
% 0.79/0.43 % Clauses deleted for lack of memory : 0
% 0.79/0.43 % Backward-subsumed : 4
% 0.79/0.43 % Backward-rewritten : 6
% 0.79/0.43 % Generated clauses : 5084
% 0.79/0.43 % ...of the previous two non-redundant : 4468
% 0.79/0.43 % ...aggressively subsumed : 0
% 0.79/0.43 % Contextual simplify-reflections : 4
% 0.79/0.43 % Paramodulations : 4592
% 0.79/0.43 % Factorizations : 12
% 0.79/0.43 % NegExts : 0
% 0.79/0.43 % Equation resolutions : 93
% 0.79/0.43 % Disequality decompositions : 0
% 0.79/0.43 % Total rewrite steps : 972
% 0.79/0.43 % ...of those cached : 712
% 0.79/0.43 % Propositional unsat checks : 0
% 0.79/0.44 % Propositional check models : 0
% 0.79/0.44 % Propositional check unsatisfiable : 0
% 0.79/0.44 % Propositional clauses : 0
% 0.79/0.44 % Propositional clauses after purity: 0
% 0.79/0.44 % Propositional unsat core size : 0
% 0.79/0.44 % Propositional preprocessing time : 0.000
% 0.79/0.44 % Propositional encoding time : 0.000
% 0.79/0.44 % Propositional solver time : 0.000
% 0.79/0.44 % Success case prop preproc time : 0.000
% 0.79/0.44 % Success case prop encoding time : 0.000
% 0.79/0.44 % Success case prop solver time : 0.000
% 0.79/0.44 % Current number of processed clauses : 375
% 0.79/0.44 % Positive orientable unit clauses : 32
% 0.79/0.44 % Positive unorientable unit clauses: 1
% 0.79/0.44 % Negative unit clauses : 24
% 0.79/0.44 % Non-unit-clauses : 318
% 0.79/0.44 % Current number of unprocessed clauses: 4293
% 0.79/0.44 % ...number of literals in the above : 14647
% 0.79/0.44 % Current number of archived formulas : 0
% 0.79/0.44 % Current number of archived clauses : 10
% 0.79/0.44 % Clause-clause subsumption calls (NU) : 17438
% 0.79/0.44 % Rec. Clause-clause subsumption calls : 9934
% 0.79/0.44 % Non-unit clause-clause subsumptions : 310
% 0.79/0.44 % Unit Clause-clause subsumption calls : 3657
% 0.79/0.44 % Rewrite failures with RHS unbound : 0
% 0.79/0.44 % BW rewrite match attempts : 12
% 0.79/0.44 % BW rewrite match successes : 4
% 0.79/0.44 % Condensation attempts : 834
% 0.79/0.44 % Condensation successes : 30
% 0.79/0.44 % Termbank termtop insertions : 172260
% 0.79/0.44 % Search garbage collected termcells : 14211
% 0.79/0.44
% 0.79/0.44 % -------------------------------------------------
% 0.79/0.44 % User time : 0.135 s
% 0.79/0.44 % System time : 0.017 s
% 0.79/0.44 % Total time : 0.152 s
% 0.79/0.44 % Maximum resident set size: 6604 pages
% 0.79/0.44
% 0.79/0.44 % -------------------------------------------------
% 0.79/0.44 % User time : 0.467 s
% 0.79/0.44 % System time : 0.053 s
% 0.79/0.44 % Total time : 0.520 s
% 0.79/0.44 % Maximum resident set size: 5376 pages
% 0.79/0.44 % E exiting
%------------------------------------------------------------------------------