%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP175^1 : 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 : n012.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 08:04:35 AM UTC 2026
% Result : Theorem 0.35s 0.26s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 44 ( 1 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 169 ( 17 ~; 10 |; 4 &; 129 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 1 ^; 20 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_Product_prod_b_b: $tType ).
thf(decl_sort2,type,
b: $tType ).
thf(decl_sort3,type,
set_b: $tType ).
thf(decl_sort4,type,
product_prod_b_b: $tType ).
thf(decl_sort5,type,
a: $tType ).
thf(decl_sort6,type,
labeled_graph_a_b: $tType ).
thf(decl_28,type,
equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).
thf(decl_38,type,
getRel_a_b: a > labeled_graph_a_b > set_Product_prod_b_b ).
thf(decl_50,type,
labeled_vertices_a_b: labeled_graph_a_b > set_b ).
thf(decl_134,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(decl_149,type,
refl_on_b: set_b > set_Product_prod_b_b > $o ).
thf(decl_150,type,
sym_b: set_Product_prod_b_b > $o ).
thf(decl_158,type,
trans_b: set_Product_prod_b_b > $o ).
thf(decl_220,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(decl_225,type,
g: labeled_graph_a_b ).
thf(decl_226,type,
i: a ).
thf(decl_228,type,
y: b ).
thf(decl_229,type,
z: b ).
thf(decl_280,type,
esk51_1: set_Product_prod_b_b > b ).
thf(decl_281,type,
esk52_1: set_Product_prod_b_b > b ).
thf(fact_264_equivE,axiom,
! [X651: set_b,X652: set_Product_prod_b_b] :
( ( equiv_equiv_b @ X651 @ X652 )
=> ~ ( ( refl_on_b @ X651 @ X652 )
=> ( ( sym_b @ X652 )
=> ~ ( trans_b @ X652 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HpgjX8aLvc/E---3.1_618634.p',fact_264_equivE) ).
thf(conj_0,conjecture,
member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ),
file('/export/starexec/sandbox2/tmp/tmp.HpgjX8aLvc/E---3.1_618634.p',conj_0) ).
thf(fact_248_sym__def,axiom,
( sym_b
= ( ^ [X613: set_Product_prod_b_b] :
! [X614: b,X615: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ X614 @ X615 ) @ X613 )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ X615 @ X614 ) @ X613 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HpgjX8aLvc/E---3.1_618634.p',fact_248_sym__def) ).
thf(fact_4_eq,axiom,
equiv_equiv_b @ ( labeled_vertices_a_b @ g ) @ ( getRel_a_b @ i @ g ),
file('/export/starexec/sandbox2/tmp/tmp.HpgjX8aLvc/E---3.1_618634.p',fact_4_eq) ).
thf(fact_1_aI,axiom,
member1285940496od_b_b @ ( product_Pair_b_b @ y @ z ) @ ( getRel_a_b @ i @ g ),
file('/export/starexec/sandbox2/tmp/tmp.HpgjX8aLvc/E---3.1_618634.p',fact_1_aI) ).
thf(c_0_5,plain,
! [X651: set_b,X652: set_Product_prod_b_b] :
( ( equiv_equiv_b @ X651 @ X652 )
=> ~ ( ( refl_on_b @ X651 @ X652 )
=> ( ( sym_b @ X652 )
=> ~ ( trans_b @ X652 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_264_equivE]) ).
thf(c_0_6,negated_conjecture,
~ ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_7,plain,
! [X1588: set_Product_prod_b_b] :
( ( sym_b @ X1588 )
<=> ! [X614: b,X615: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ X614 @ X615 ) @ X1588 )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ X615 @ X614 ) @ X1588 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_248_sym__def])]) ).
thf(c_0_8,plain,
! [X1772: set_b,X1773: set_Product_prod_b_b] :
( ( ( refl_on_b @ X1772 @ X1773 )
| ~ ( equiv_equiv_b @ X1772 @ X1773 ) )
& ( ( sym_b @ X1773 )
| ~ ( equiv_equiv_b @ X1772 @ X1773 ) )
& ( ( trans_b @ X1773 )
| ~ ( equiv_equiv_b @ X1772 @ X1773 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_9,negated_conjecture,
~ ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
thf(c_0_10,plain,
! [X1979: set_Product_prod_b_b,X1980: b,X1981: b,X1982: set_Product_prod_b_b] :
( ( ~ ( sym_b @ X1979 )
| ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ X1980 @ X1981 ) @ X1979 )
| ( member1285940496od_b_b @ ( product_Pair_b_b @ X1981 @ X1980 ) @ X1979 ) )
& ( ( member1285940496od_b_b @ ( product_Pair_b_b @ ( esk51_1 @ X1982 ) @ ( esk52_1 @ X1982 ) ) @ X1982 )
| ( sym_b @ X1982 ) )
& ( ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ ( esk52_1 @ X1982 ) @ ( esk51_1 @ X1982 ) ) @ X1982 )
| ( sym_b @ X1982 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])])])]) ).
thf(c_0_11,plain,
! [X170: set_b,X166: set_Product_prod_b_b] :
( ( sym_b @ X166 )
| ~ ( equiv_equiv_b @ X170 @ X166 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
equiv_equiv_b @ ( labeled_vertices_a_b @ g ) @ ( getRel_a_b @ i @ g ),
inference(split_conjunct,[status(thm)],[fact_4_eq]) ).
thf(c_0_13,negated_conjecture,
~ ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: b,X2: b,X166: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ X2 @ X1 ) @ X166 )
| ~ ( sym_b @ X166 )
| ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ X1 @ X2 ) @ X166 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
member1285940496od_b_b @ ( product_Pair_b_b @ y @ z ) @ ( getRel_a_b @ i @ g ),
inference(split_conjunct,[status(thm)],[fact_1_aI]) ).
thf(c_0_16,plain,
sym_b @ ( getRel_a_b @ i @ g ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,negated_conjecture,
~ ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP175^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 20:06:03 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.17 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.HpgjX8aLvc/E---3.1_618634.p
% 0.35/0.26 % Version: 3.5.1-ho
% 0.35/0.26 % Preprocessing class: HSLMSMSMSSMNSFA.
% 0.35/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.35/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.35/0.26 % Starting full_lambda_6 with 300s (1) cores
% 0.35/0.26 % Starting ehoh_best_sine with 300s (1) cores
% 0.35/0.26 % ehoh_best_sine_rwall with pid 618648 completed with status 0
% 0.35/0.26 % Result found by ehoh_best_sine_rwall
% 0.35/0.26 % Preprocessing class: HSLMSMSMSSMNSFA.
% 0.35/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.35/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.35/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.35/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.35/0.26 % Search class: HGHSM-FSLM31-MSFFFFBN
% 0.35/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.35/0.26 % SubtermCWHack with pid 618652 completed with status 0
% 0.35/0.26 % Result found by SubtermCWHack
% 0.35/0.26 % Preprocessing class: HSLMSMSMSSMNSFA.
% 0.35/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.35/0.26 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.35/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.35/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.35/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.35/0.26 % Search class: HGHSM-FSLM31-MSFFFFBN
% 0.35/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.35/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.35/0.26 % Preprocessing time : 0.004 s
% 0.35/0.26
% 0.35/0.26 % Proof found!
% 0.35/0.26 % SZS status Theorem
% 0.35/0.26 % SZS output start CNFRefutation
% See solution above
% 0.35/0.26 % Parsed axioms : 639
% 0.35/0.26 % Removed by relevancy pruning/SinE : 368
% 0.35/0.26 % Initial clauses : 436
% 0.35/0.26 % Removed in clause preprocessing : 18
% 0.35/0.26 % Initial clauses in saturation : 418
% 0.35/0.26 % Processed clauses : 1364
% 0.35/0.26 % ...of these trivial : 52
% 0.35/0.26 % ...subsumed : 798
% 0.35/0.26 % ...remaining for further processing : 514
% 0.35/0.26 % Other redundant clauses eliminated : 164
% 0.35/0.26 % Clauses deleted for lack of memory : 0
% 0.35/0.26 % Backward-subsumed : 4
% 0.35/0.26 % Backward-rewritten : 40
% 0.35/0.26 % Generated clauses : 3592
% 0.35/0.26 % ...of the previous two non-redundant : 2246
% 0.35/0.26 % ...aggressively subsumed : 0
% 0.35/0.26 % Contextual simplify-reflections : 1
% 0.35/0.26 % Paramodulations : 3411
% 0.35/0.26 % Factorizations : 2
% 0.35/0.26 % NegExts : 0
% 0.35/0.26 % Equation resolutions : 180
% 0.35/0.26 % Disequality decompositions : 0
% 0.35/0.26 % Total rewrite steps : 1342
% 0.35/0.26 % ...of those cached : 1109
% 0.35/0.26 % Propositional unsat checks : 0
% 0.35/0.26 % Propositional check models : 0
% 0.35/0.26 % Propositional check unsatisfiable : 0
% 0.35/0.26 % Propositional clauses : 0
% 0.35/0.26 % Propositional clauses after purity: 0
% 0.35/0.26 % Propositional unsat core size : 0
% 0.35/0.26 % Propositional preprocessing time : 0.000
% 0.35/0.26 % Propositional encoding time : 0.000
% 0.35/0.26 % Propositional solver time : 0.000
% 0.35/0.26 % Success case prop preproc time : 0.000
% 0.35/0.26 % Success case prop encoding time : 0.000
% 0.35/0.26 % Success case prop solver time : 0.000
% 0.35/0.26 % Current number of processed clauses : 442
% 0.35/0.26 % Positive orientable unit clauses : 133
% 0.35/0.26 % Positive unorientable unit clauses: 1
% 0.35/0.26 % Negative unit clauses : 6
% 0.35/0.26 % Non-unit-clauses : 302
% 0.35/0.26 % Current number of unprocessed clauses: 1249
% 0.35/0.26 % ...number of literals in the above : 3313
% 0.35/0.26 % Current number of archived formulas : 0
% 0.35/0.26 % Current number of archived clauses : 44
% 0.35/0.26 % Clause-clause subsumption calls (NU) : 19949
% 0.35/0.26 % Rec. Clause-clause subsumption calls : 15996
% 0.35/0.26 % Non-unit clause-clause subsumptions : 761
% 0.35/0.26 % Unit Clause-clause subsumption calls : 3451
% 0.35/0.26 % Rewrite failures with RHS unbound : 0
% 0.35/0.26 % BW rewrite match attempts : 80
% 0.35/0.26 % BW rewrite match successes : 43
% 0.35/0.26 % Condensation attempts : 0
% 0.35/0.26 % Condensation successes : 0
% 0.35/0.26 % Termbank termtop insertions : 66076
% 0.35/0.26 % Search garbage collected termcells : 11295
% 0.35/0.26
% 0.35/0.26 % -------------------------------------------------
% 0.35/0.26 % User time : 0.059 s
% 0.35/0.26 % System time : 0.008 s
% 0.35/0.26 % Total time : 0.067 s
% 0.35/0.26 % Maximum resident set size: 6680 pages
% 0.35/0.26
% 0.35/0.26 % -------------------------------------------------
% 0.35/0.26 % User time : 0.068 s
% 0.35/0.26 % System time : 0.011 s
% 0.35/0.26 % Total time : 0.079 s
% 0.35/0.26 % Maximum resident set size: 6144 pages
% 0.35/0.26 % E exiting
%------------------------------------------------------------------------------