%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP081^1 : 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 : n026.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 08:04:18 AM UTC 2026
% Result : Theorem 6.24s 1.42s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 373 ( 12 ~; 7 |; 0 &; 351 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 9 con; 0-7 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_val: $tType ).
thf(decl_sort2,type,
g: $tType ).
thf(decl_sort3,type,
list_node: $tType ).
thf(decl_sort4,type,
node: $tType ).
thf(decl_sort5,type,
list_P561207620_edgeD: $tType ).
thf(decl_sort6,type,
val: $tType ).
thf(decl_sort7,type,
produc1432036078de_val: $tType ).
thf(decl_sort8,type,
option_list_val: $tType ).
thf(decl_25,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(decl_29,type,
append_node: list_node > list_node > list_node ).
thf(decl_40,type,
hd_node: list_node > node ).
thf(decl_46,type,
tl_node: list_node > list_node ).
thf(decl_51,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(decl_60,type,
alpha_n: g > list_node ).
thf(decl_61,type,
phi_r: val ).
thf(decl_62,type,
defs: g > node > set_val ).
thf(decl_63,type,
g2: g ).
thf(decl_64,type,
i: node ).
thf(decl_65,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(decl_66,type,
invar: g > $o ).
thf(decl_70,type,
n: node ).
thf(decl_71,type,
ns: list_node ).
thf(decl_72,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(decl_74,type,
r: val ).
thf(decl_75,type,
ri: list_node ).
thf(decl_77,type,
rs2: list_node ).
thf(fact_264_old_Opath2__hd,axiom,
! [X1: g,X2: node,X3: list_node,X4: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ X3 @ X4 )
=> ( X2
= ( hd_node @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',fact_264_old_Opath2__hd) ).
thf(fact_9_rs__props_I1_J,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',fact_9_rs__props_I1_J) ).
thf(fact_1_ri__is__valid,axiom,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',fact_1_ri__is__valid) ).
thf(fact_4_ri__props_I1_J,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',fact_4_ri__props_I1_J) ).
thf(conj_0,conjecture,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',conj_0) ).
thf(fact_5_old_Opath2__app,axiom,
! [X1: g,X2: node,X3: list_node,X4: node,X5: list_node,X6: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ X3 @ X4 )
=> ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X4 @ X5 @ X6 )
=> ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ ( append_node @ X3 @ ( tl_node @ X5 ) ) @ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',fact_5_old_Opath2__app) ).
thf(fact_3_assms_I7_J,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
file('/export/starexec/sandbox2/tmp/tmp.MOE22dVIU8/E---3.1_1096088.p',fact_3_assms_I7_J) ).
thf(c_0_7,plain,
! [X3136: g,X3137: node,X3138: list_node,X3139: node] :
( ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3136 @ X3137 @ X3138 @ X3139 )
| ( X3137
= ( hd_node @ X3138 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_264_old_Opath2__hd])])]) ).
thf(c_0_8,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ),
inference(split_conjunct,[status(thm)],[fact_9_rs__props_I1_J]) ).
thf(c_0_9,plain,
( i
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(split_conjunct,[status(thm)],[fact_1_ri__is__valid]) ).
thf(c_0_10,plain,
! [X3: list_node,X2: node,X1: g,X4: node] :
( ( X2
= ( hd_node @ X3 ) )
| ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ri @ i,
inference(split_conjunct,[status(thm)],[fact_4_ri__props_I1_J]) ).
thf(c_0_12,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_13,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs2 @ i,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_14,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r )
= ( hd_node @ ri ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(fof_simplification,[status(thm)],[c_0_12]) ).
thf(c_0_16,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( hd_node @ ri ) @ rs2 @ i,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
thf(c_0_18,plain,
! [X2038: g,X2039: node,X2040: list_node,X2041: node,X2042: list_node,X2043: node] :
( ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2038 @ X2039 @ X2040 @ X2041 )
| ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2038 @ X2041 @ X2042 @ X2043 )
| ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2038 @ X2039 @ ( append_node @ X2040 @ ( tl_node @ X2042 ) ) @ X2043 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_old_Opath2__app])])]) ).
thf(c_0_19,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( hd_node @ ri ) @ ri @ i,
inference(rw,[status(thm)],[c_0_11,c_0_14]) ).
thf(c_0_20,plain,
( ( hd_node @ ri )
= ( hd_node @ rs2 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
thf(c_0_21,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ),
inference(split_conjunct,[status(thm)],[fact_3_assms_I7_J]) ).
thf(c_0_22,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,plain,
! [X3: list_node,X2: node,X1: g,X4: node,X5: list_node,X6: node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ ( append_node @ X3 @ ( tl_node @ X5 ) ) @ X6 )
| ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X2 @ X3 @ X4 )
| ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X1 @ X4 @ X5 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( hd_node @ rs2 ) @ ri @ i,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_25,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( hd_node @ ri ),
inference(rw,[status(thm)],[c_0_21,c_0_14]) ).
thf(c_0_26,negated_conjecture,
~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ( append_node @ ns @ ( tl_node @ ri ) ) @ i ),
inference(rw,[status(thm)],[c_0_22,c_0_9]) ).
thf(c_0_27,plain,
! [X2: node,X3: list_node] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X2 @ ( append_node @ X3 @ ( tl_node @ ri ) ) @ i )
| ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ X2 @ X3 @ ( hd_node @ rs2 ) ) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_28,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( hd_node @ rs2 ),
inference(rw,[status(thm)],[c_0_25,c_0_20]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP081^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n026.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 19:51:42 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.22/0.27 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.MOE22dVIU8/E---3.1_1096088.p
% 6.24/1.42 % Version: 3.5.1-ho
% 6.24/1.42 % Preprocessing class: HSLSSMSMSSMNHSA.
% 6.24/1.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.24/1.42 % Starting ehoh_best2 with 1500s (5) cores
% 6.24/1.42 % Starting additional_ho_6 with 300s (1) cores
% 6.24/1.42 % Starting new_bool_5 with 300s (1) cores
% 6.24/1.42 % Starting new_bool_1 with 300s (1) cores
% 6.24/1.42 % ehoh_best2 with pid 1096101 completed with status 0
% 6.24/1.42 % Result found by ehoh_best2
% 6.24/1.42 % Preprocessing class: HSLSSMSMSSMNHSA.
% 6.24/1.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.24/1.42 % Starting ehoh_best2 with 1500s (5) cores
% 6.24/1.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.24/1.42 % No SInE strategy applied
% 6.24/1.42 % Search class: HGHSM-FSLM31-MHSFFSBN
% 6.24/1.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.24/1.42 % Starting SubtermCWHack with 136s (1) cores
% 6.24/1.42 % Starting ehoh_best2 with 151s (1) cores
% 6.24/1.42 % Starting lpo4_lambdas_fix with 136s (1) cores
% 6.24/1.42 % Starting post_as_ho3 with 136s (1) cores
% 6.24/1.42 % Starting full_lambda_10 with 136s (1) cores
% 6.24/1.42 % full_lambda_10 with pid 1096112 completed with status 0
% 6.24/1.42 % Result found by full_lambda_10
% 6.24/1.42 % Preprocessing class: HSLSSMSMSSMNHSA.
% 6.24/1.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.24/1.42 % Starting ehoh_best2 with 1500s (5) cores
% 6.24/1.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.24/1.42 % No SInE strategy applied
% 6.24/1.42 % Search class: HGHSM-FSLM31-MHSFFSBN
% 6.24/1.42 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 6.24/1.42 % Starting SubtermCWHack with 136s (1) cores
% 6.24/1.42 % Starting ehoh_best2 with 151s (1) cores
% 6.24/1.42 % Starting lpo4_lambdas_fix with 136s (1) cores
% 6.24/1.42 % Starting post_as_ho3 with 136s (1) cores
% 6.24/1.42 % Starting full_lambda_10 with 136s (1) cores
% 6.24/1.42 % Preprocessing time : 0.020 s
% 6.24/1.42 % Presaturation interreduction done
% 6.24/1.42
% 6.24/1.42 % Proof found!
% 6.24/1.42 % SZS status Theorem
% 6.24/1.42 % SZS output start CNFRefutation
% See solution above
% 6.24/1.42 % Parsed axioms : 419
% 6.24/1.42 % Removed by relevancy pruning/SinE : 0
% 6.24/1.42 % Initial clauses : 904
% 6.24/1.42 % Removed in clause preprocessing : 99
% 6.24/1.42 % Initial clauses in saturation : 805
% 6.24/1.42 % Processed clauses : 2163
% 6.24/1.42 % ...of these trivial : 55
% 6.24/1.42 % ...subsumed : 354
% 6.24/1.42 % ...remaining for further processing : 1754
% 6.24/1.42 % Other redundant clauses eliminated : 2731
% 6.24/1.42 % Clauses deleted for lack of memory : 0
% 6.24/1.42 % Backward-subsumed : 23
% 6.24/1.42 % Backward-rewritten : 23
% 6.24/1.42 % Generated clauses : 17072
% 6.24/1.42 % ...of the previous two non-redundant : 13737
% 6.24/1.42 % ...aggressively subsumed : 0
% 6.24/1.42 % Contextual simplify-reflections : 2
% 6.24/1.42 % Paramodulations : 14326
% 6.24/1.42 % Factorizations : 4
% 6.24/1.42 % NegExts : 0
% 6.24/1.42 % Equation resolutions : 2773
% 6.24/1.42 % Disequality decompositions : 0
% 6.24/1.42 % Total rewrite steps : 1583
% 6.24/1.42 % ...of those cached : 1128
% 6.24/1.42 % Propositional unsat checks : 0
% 6.24/1.42 % Propositional check models : 0
% 6.24/1.42 % Propositional check unsatisfiable : 0
% 6.24/1.42 % Propositional clauses : 0
% 6.24/1.42 % Propositional clauses after purity: 0
% 6.24/1.42 % Propositional unsat core size : 0
% 6.24/1.42 % Propositional preprocessing time : 0.000
% 6.24/1.42 % Propositional encoding time : 0.000
% 6.24/1.42 % Propositional solver time : 0.000
% 6.24/1.42 % Success case prop preproc time : 0.000
% 6.24/1.42 % Success case prop encoding time : 0.000
% 6.24/1.42 % Success case prop solver time : 0.000
% 6.24/1.42 % Current number of processed clauses : 960
% 6.24/1.42 % Positive orientable unit clauses : 164
% 6.24/1.42 % Positive unorientable unit clauses: 0
% 6.24/1.42 % Negative unit clauses : 71
% 6.24/1.42 % Non-unit-clauses : 725
% 6.24/1.42 % Current number of unprocessed clauses: 12857
% 6.24/1.42 % ...number of literals in the above : 45117
% 6.24/1.42 % Current number of archived formulas : 0
% 6.24/1.42 % Current number of archived clauses : 662
% 6.24/1.42 % Clause-clause subsumption calls (NU) : 158630
% 6.24/1.42 % Rec. Clause-clause subsumption calls : 60259
% 6.24/1.42 % Non-unit clause-clause subsumptions : 212
% 6.24/1.42 % Unit Clause-clause subsumption calls : 7842
% 6.24/1.42 % Rewrite failures with RHS unbound : 0
% 6.24/1.42 % BW rewrite match attempts : 308
% 6.24/1.42 % BW rewrite match successes : 7
% 6.24/1.42 % Condensation attempts : 2163
% 6.24/1.42 % Condensation successes : 1
% 6.24/1.42 % Termbank termtop insertions : 997539
% 6.24/1.42 % Search garbage collected termcells : 21063
% 6.24/1.42
% 6.24/1.42 % -------------------------------------------------
% 6.24/1.42 % User time : 0.880 s
% 6.24/1.42 % System time : 0.028 s
% 6.24/1.42 % Total time : 0.908 s
% 6.24/1.42 % Maximum resident set size: 8064 pages
% 6.24/1.42
% 6.24/1.42 % -------------------------------------------------
% 6.24/1.42 % User time : 4.232 s
% 6.24/1.42 % System time : 0.155 s
% 6.24/1.42 % Total time : 4.387 s
% 6.24/1.42 % Maximum resident set size: 5632 pages
% 6.24/1.42 % E exiting
%------------------------------------------------------------------------------