%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP080^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 1.43s 0.59s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 176 ( 13 ~; 6 |; 0 &; 153 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 5 con; 0-7 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
val: $tType ).
thf(decl_sort2,type,
set_node: $tType ).
thf(decl_sort3,type,
set_val: $tType ).
thf(decl_sort4,type,
g: $tType ).
thf(decl_sort5,type,
list_node: $tType ).
thf(decl_sort6,type,
node: $tType ).
thf(decl_sort7,type,
list_P561207620_edgeD: $tType ).
thf(decl_sort8,type,
produc1432036078de_val: $tType ).
thf(decl_sort9,type,
option_list_val: $tType ).
thf(decl_25,type,
graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
thf(decl_29,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(decl_35,type,
distinct_node: list_node > $o ).
thf(decl_48,type,
hd_node: list_node > node ).
thf(decl_51,type,
set_node2: list_node > set_node ).
thf(decl_54,type,
tl_node: list_node > list_node ).
thf(decl_61,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(decl_69,type,
member_node: node > set_node > $o ).
thf(decl_71,type,
entry: g > node ).
thf(decl_72,type,
alpha_n: g > list_node ).
thf(decl_74,type,
defs: g > node > set_val ).
thf(decl_75,type,
g2: g ).
thf(decl_76,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(decl_77,type,
invar: g > $o ).
thf(decl_82,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(decl_83,type,
pred_phi_r: node ).
thf(decl_84,type,
r: val ).
thf(decl_85,type,
rs: list_node ).
thf(conj_0,conjecture,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
file('/export/starexec/sandbox/tmp/tmp.P8wogfkzGJ/E---3.1_3835175.p',conj_0) ).
thf(fact_0_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/sandbox/tmp/tmp.P8wogfkzGJ/E---3.1_3835175.p',fact_0_old_Opath2__hd) ).
thf(fact_30_FormalSSA__Misc_Odistinct__hd__tl,axiom,
! [X17: list_node] :
( ( distinct_node @ X17 )
=> ~ ( member_node @ ( hd_node @ X17 ) @ ( set_node2 @ ( tl_node @ X17 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.P8wogfkzGJ/E---3.1_3835175.p',fact_30_FormalSSA__Misc_Odistinct__hd__tl) ).
thf(fact_4_rs_H__props_I1_J,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
file('/export/starexec/sandbox/tmp/tmp.P8wogfkzGJ/E---3.1_3835175.p',fact_4_rs_H__props_I1_J) ).
thf(fact_5_old_OEntryPath__distinct,axiom,
! [X1: g,X3: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X1 @ X3 )
=> ( distinct_node @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.P8wogfkzGJ/E---3.1_3835175.p',fact_5_old_OEntryPath__distinct) ).
thf(fact_3_rs_H__props_I2_J,axiom,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
file('/export/starexec/sandbox/tmp/tmp.P8wogfkzGJ/E---3.1_3835175.p',fact_3_rs_H__props_I2_J) ).
thf(c_0_6,negated_conjecture,
~ ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,plain,
! [X2338: g,X2339: node,X2340: list_node,X2341: node] :
( ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X2338 @ X2339 @ X2340 @ X2341 )
| ( X2339
= ( hd_node @ X2340 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_old_Opath2__hd])])]) ).
thf(c_0_8,plain,
! [X17: list_node] :
( ( distinct_node @ X17 )
=> ~ ( member_node @ ( hd_node @ X17 ) @ ( set_node2 @ ( tl_node @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_30_FormalSSA__Misc_Odistinct__hd__tl]) ).
thf(c_0_9,negated_conjecture,
member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
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 ) @ rs @ pred_phi_r,
inference(split_conjunct,[status(thm)],[fact_4_rs_H__props_I1_J]) ).
thf(c_0_12,plain,
! [X2343: g,X2344: list_node] :
( ~ ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X2343 @ X2344 )
| ( distinct_node @ X2344 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_old_OEntryPath__distinct])])]) ).
thf(c_0_13,plain,
! [X2405: list_node] :
( ~ ( distinct_node @ X2405 )
| ~ ( member_node @ ( hd_node @ X2405 ) @ ( set_node2 @ ( tl_node @ X2405 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
thf(c_0_14,negated_conjecture,
member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_15,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r )
= ( hd_node @ rs ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_16,plain,
! [X1: g,X3: list_node] :
( ( distinct_node @ X3 )
| ~ ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
inference(split_conjunct,[status(thm)],[fact_3_rs_H__props_I2_J]) ).
thf(c_0_18,plain,
! [X3: list_node] :
( ~ ( distinct_node @ X3 )
| ~ ( member_node @ ( hd_node @ X3 ) @ ( set_node2 @ ( tl_node @ X3 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
member_node @ ( hd_node @ rs ) @ ( set_node2 @ ( tl_node @ rs ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,plain,
distinct_node @ rs,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP080^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.15 % Computer : n007.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Sep 29 19:46:41 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 Running higher-order theorem proving
% 0.15/0.26 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.P8wogfkzGJ/E---3.1_3835175.p
% 1.43/0.59 % Version: 3.5.1-ho
% 1.43/0.59 % Preprocessing class: HSLSSMSMSSMNHSA.
% 1.43/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.43/0.59 % Starting ehoh_best2 with 1500s (5) cores
% 1.43/0.59 % Starting additional_ho_6 with 300s (1) cores
% 1.43/0.59 % Starting new_bool_5 with 300s (1) cores
% 1.43/0.59 % Starting new_bool_1 with 300s (1) cores
% 1.43/0.59 % ehoh_best2 with pid 3835188 completed with status 0
% 1.43/0.59 % Result found by ehoh_best2
% 1.43/0.59 % Preprocessing class: HSLSSMSMSSMNHSA.
% 1.43/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.43/0.59 % Starting ehoh_best2 with 1500s (5) cores
% 1.43/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.43/0.59 % No SInE strategy applied
% 1.43/0.59 % Search class: HGHSM-FSLM31-DHSFFSBN
% 1.43/0.59 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.43/0.59 % Starting SubtermCWHack with 151s (1) cores
% 1.43/0.59 % Starting ehoh_best2 with 901s (1) cores
% 1.43/0.59 % Starting ehoh_best7 with 151s (1) cores
% 1.43/0.59 % Starting sh7 with 151s (1) cores
% 1.43/0.59 % Starting new_ho_10 with 146s (1) cores
% 1.43/0.59 % new_ho_10 with pid 3835199 completed with status 0
% 1.43/0.59 % Result found by new_ho_10
% 1.43/0.59 % Preprocessing class: HSLSSMSMSSMNHSA.
% 1.43/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.43/0.59 % Starting ehoh_best2 with 1500s (5) cores
% 1.43/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.43/0.59 % No SInE strategy applied
% 1.43/0.59 % Search class: HGHSM-FSLM31-DHSFFSBN
% 1.43/0.59 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 1.43/0.59 % Starting SubtermCWHack with 151s (1) cores
% 1.43/0.59 % Starting ehoh_best2 with 901s (1) cores
% 1.43/0.59 % Starting ehoh_best7 with 151s (1) cores
% 1.43/0.59 % Starting sh7 with 151s (1) cores
% 1.43/0.59 % Starting new_ho_10 with 146s (1) cores
% 1.43/0.59 % Preprocessing time : 0.019 s
% 1.43/0.59 % Presaturation interreduction done
% 1.43/0.59
% 1.43/0.59 % Proof found!
% 1.43/0.59 % SZS status Theorem
% 1.43/0.59 % SZS output start CNFRefutation
% See solution above
% 1.43/0.59 % Parsed axioms : 432
% 1.43/0.59 % Removed by relevancy pruning/SinE : 0
% 1.43/0.59 % Initial clauses : 956
% 1.43/0.59 % Removed in clause preprocessing : 97
% 1.43/0.59 % Initial clauses in saturation : 859
% 1.43/0.59 % Processed clauses : 1131
% 1.43/0.59 % ...of these trivial : 20
% 1.43/0.59 % ...subsumed : 102
% 1.43/0.59 % ...remaining for further processing : 1009
% 1.43/0.59 % Other redundant clauses eliminated : 214
% 1.43/0.59 % Clauses deleted for lack of memory : 0
% 1.43/0.59 % Backward-subsumed : 2
% 1.43/0.59 % Backward-rewritten : 8
% 1.43/0.59 % Generated clauses : 726
% 1.43/0.59 % ...of the previous two non-redundant : 498
% 1.43/0.59 % ...aggressively subsumed : 0
% 1.43/0.59 % Contextual simplify-reflections : 3
% 1.43/0.59 % Paramodulations : 552
% 1.43/0.59 % Factorizations : 0
% 1.43/0.59 % NegExts : 0
% 1.43/0.59 % Equation resolutions : 218
% 1.43/0.59 % Disequality decompositions : 0
% 1.43/0.59 % Total rewrite steps : 264
% 1.43/0.59 % ...of those cached : 182
% 1.43/0.59 % Propositional unsat checks : 0
% 1.43/0.59 % Propositional check models : 0
% 1.43/0.59 % Propositional check unsatisfiable : 0
% 1.43/0.59 % Propositional clauses : 0
% 1.43/0.59 % Propositional clauses after purity: 0
% 1.43/0.59 % Propositional unsat core size : 0
% 1.43/0.59 % Propositional preprocessing time : 0.000
% 1.43/0.59 % Propositional encoding time : 0.000
% 1.43/0.59 % Propositional solver time : 0.000
% 1.43/0.59 % Success case prop preproc time : 0.000
% 1.43/0.59 % Success case prop encoding time : 0.000
% 1.43/0.59 % Success case prop solver time : 0.000
% 1.43/0.59 % Current number of processed clauses : 196
% 1.43/0.59 % Positive orientable unit clauses : 61
% 1.43/0.59 % Positive unorientable unit clauses: 0
% 1.43/0.59 % Negative unit clauses : 18
% 1.43/0.59 % Non-unit-clauses : 117
% 1.43/0.59 % Current number of unprocessed clauses: 894
% 1.43/0.59 % ...number of literals in the above : 2952
% 1.43/0.59 % Current number of archived formulas : 0
% 1.43/0.59 % Current number of archived clauses : 684
% 1.43/0.59 % Clause-clause subsumption calls (NU) : 100650
% 1.43/0.59 % Rec. Clause-clause subsumption calls : 17913
% 1.43/0.59 % Non-unit clause-clause subsumptions : 87
% 1.43/0.59 % Unit Clause-clause subsumption calls : 258
% 1.43/0.59 % Rewrite failures with RHS unbound : 0
% 1.43/0.59 % BW rewrite match attempts : 32
% 1.43/0.59 % BW rewrite match successes : 1
% 1.43/0.59 % Condensation attempts : 1131
% 1.43/0.59 % Condensation successes : 0
% 1.43/0.59 % Termbank termtop insertions : 124936
% 1.43/0.59 % Search garbage collected termcells : 26223
% 1.43/0.59
% 1.43/0.59 % -------------------------------------------------
% 1.43/0.59 % User time : 0.265 s
% 1.43/0.59 % System time : 0.018 s
% 1.43/0.59 % Total time : 0.283 s
% 1.43/0.59 % Maximum resident set size: 8892 pages
% 1.43/0.59
% 1.43/0.59 % -------------------------------------------------
% 1.43/0.59 % User time : 1.030 s
% 1.43/0.59 % System time : 0.074 s
% 1.43/0.59 % Total time : 1.104 s
% 1.43/0.59 % Maximum resident set size: 6144 pages
% 1.43/0.59 % E exiting
%------------------------------------------------------------------------------