%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP175^1 : 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 : n017.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 08:05:45 AM UTC 2026
% Result : Theorem 0.53s 0.40s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 0 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 141 ( 16 ~; 8 |; 2 &; 107 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% 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(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/sandbox/tmp/tmp.3BhUOHTKSt/E---3.1_826789.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/sandbox/tmp/tmp.3BhUOHTKSt/E---3.1_826789.p',conj_0) ).
thf(fact_250_symE,axiom,
! [X619: set_Product_prod_b_b,X620: b,X621: b] :
( ( sym_b @ X619 )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X620 @ X621 ) @ X619 )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ X621 @ X620 ) @ X619 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3BhUOHTKSt/E---3.1_826789.p',fact_250_symE) ).
thf(fact_4_eq,axiom,
equiv_equiv_b @ ( labeled_vertices_a_b @ g ) @ ( getRel_a_b @ i @ g ),
file('/export/starexec/sandbox/tmp/tmp.3BhUOHTKSt/E---3.1_826789.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/sandbox/tmp/tmp.3BhUOHTKSt/E---3.1_826789.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,
! [X1603: set_b,X1604: set_Product_prod_b_b] :
( ( ( refl_on_b @ X1603 @ X1604 )
| ~ ( equiv_equiv_b @ X1603 @ X1604 ) )
& ( ( sym_b @ X1604 )
| ~ ( equiv_equiv_b @ X1603 @ X1604 ) )
& ( ( trans_b @ X1604 )
| ~ ( equiv_equiv_b @ X1603 @ X1604 ) ) ),
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_8,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_9,plain,
! [X1801: set_Product_prod_b_b,X1802: b,X1803: b] :
( ~ ( sym_b @ X1801 )
| ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ X1802 @ X1803 ) @ X1801 )
| ( member1285940496od_b_b @ ( product_Pair_b_b @ X1803 @ X1802 ) @ X1801 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_250_symE])])]) ).
thf(c_0_10,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_7]) ).
thf(c_0_11,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_12,negated_conjecture,
~ ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ),
inference(fof_nnf,[status(thm)],[c_0_8]) ).
thf(c_0_13,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_9]) ).
thf(c_0_14,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_15,plain,
sym_b @ ( getRel_a_b @ i @ g ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_16,negated_conjecture,
~ ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP175^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n017.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 20:01:52 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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.3BhUOHTKSt/E---3.1_826789.p
% 0.53/0.40 % Version: 3.5.1-ho
% 0.53/0.40 % Preprocessing class: HSLMSMSMSSMNSFA.
% 0.53/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.40 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.53/0.40 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.53/0.40 % Starting full_lambda_6 with 300s (1) cores
% 0.53/0.40 % Starting ehoh_best_sine with 300s (1) cores
% 0.53/0.40 % full_lambda_6 with pid 826804 completed with status 0
% 0.53/0.40 % Result found by full_lambda_6
% 0.53/0.40 % Preprocessing class: HSLMSMSMSSMNSFA.
% 0.53/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.40 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.53/0.40 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.53/0.40 % Starting full_lambda_6 with 300s (1) cores
% 0.53/0.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.53/0.40 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.53/0.40 % Search class: HGHSM-FSLM31-DSFFFFBN
% 0.53/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.53/0.40 % SubtermCWHack with pid 826806 completed with status 0
% 0.53/0.40 % Result found by SubtermCWHack
% 0.53/0.40 % Preprocessing class: HSLMSMSMSSMNSFA.
% 0.53/0.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.40 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.53/0.40 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.53/0.40 % Starting full_lambda_6 with 300s (1) cores
% 0.53/0.40 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,4,,4,20000,1.0,true))
% 0.53/0.40 % SinE strategy is GSinE(CountTerms,hypos,4,,4,20000,1.0,true)
% 0.53/0.40 % Search class: HGHSM-FSLM31-DSFFFFBN
% 0.53/0.40 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.53/0.40 % Starting SubtermCWHack with 28s (1) cores
% 0.53/0.40 % Preprocessing time : 0.007 s
% 0.53/0.40
% 0.53/0.40 % Proof found!
% 0.53/0.40 % SZS status Theorem
% 0.53/0.40 % SZS output start CNFRefutation
% See solution above
% 0.53/0.40 % Parsed axioms : 639
% 0.53/0.40 % Removed by relevancy pruning/SinE : 398
% 0.53/0.40 % Initial clauses : 363
% 0.53/0.40 % Removed in clause preprocessing : 18
% 0.53/0.40 % Initial clauses in saturation : 345
% 0.53/0.40 % Processed clauses : 1254
% 0.53/0.40 % ...of these trivial : 51
% 0.53/0.40 % ...subsumed : 754
% 0.53/0.40 % ...remaining for further processing : 449
% 0.53/0.40 % Other redundant clauses eliminated : 164
% 0.53/0.40 % Clauses deleted for lack of memory : 0
% 0.53/0.40 % Backward-subsumed : 4
% 0.53/0.40 % Backward-rewritten : 42
% 0.53/0.40 % Generated clauses : 3387
% 0.53/0.40 % ...of the previous two non-redundant : 2089
% 0.53/0.40 % ...aggressively subsumed : 0
% 0.53/0.40 % Contextual simplify-reflections : 1
% 0.53/0.40 % Paramodulations : 3204
% 0.53/0.40 % Factorizations : 2
% 0.53/0.40 % NegExts : 0
% 0.53/0.40 % Equation resolutions : 180
% 0.53/0.40 % Disequality decompositions : 0
% 0.53/0.40 % Total rewrite steps : 1279
% 0.53/0.40 % ...of those cached : 1079
% 0.53/0.40 % Propositional unsat checks : 0
% 0.53/0.40 % Propositional check models : 0
% 0.53/0.40 % Propositional check unsatisfiable : 0
% 0.53/0.40 % Propositional clauses : 0
% 0.53/0.40 % Propositional clauses after purity: 0
% 0.53/0.40 % Propositional unsat core size : 0
% 0.53/0.40 % Propositional preprocessing time : 0.000
% 0.53/0.40 % Propositional encoding time : 0.000
% 0.53/0.40 % Propositional solver time : 0.000
% 0.53/0.40 % Success case prop preproc time : 0.000
% 0.53/0.40 % Success case prop encoding time : 0.000
% 0.53/0.40 % Success case prop solver time : 0.000
% 0.53/0.40 % Current number of processed clauses : 375
% 0.53/0.40 % Positive orientable unit clauses : 120
% 0.53/0.40 % Positive unorientable unit clauses: 1
% 0.53/0.40 % Negative unit clauses : 6
% 0.53/0.40 % Non-unit-clauses : 248
% 0.53/0.40 % Current number of unprocessed clauses: 1128
% 0.53/0.40 % ...number of literals in the above : 2954
% 0.53/0.40 % Current number of archived formulas : 0
% 0.53/0.40 % Current number of archived clauses : 46
% 0.53/0.40 % Clause-clause subsumption calls (NU) : 12297
% 0.53/0.40 % Rec. Clause-clause subsumption calls : 10777
% 0.53/0.40 % Non-unit clause-clause subsumptions : 717
% 0.53/0.40 % Unit Clause-clause subsumption calls : 1414
% 0.53/0.40 % Rewrite failures with RHS unbound : 0
% 0.53/0.40 % BW rewrite match attempts : 81
% 0.53/0.40 % BW rewrite match successes : 44
% 0.53/0.40 % Condensation attempts : 0
% 0.53/0.40 % Condensation successes : 0
% 0.53/0.40 % Termbank termtop insertions : 58685
% 0.53/0.40 % Search garbage collected termcells : 9826
% 0.53/0.40
% 0.53/0.40 % -------------------------------------------------
% 0.53/0.40 % User time : 0.083 s
% 0.53/0.40 % System time : 0.012 s
% 0.53/0.40 % Total time : 0.094 s
% 0.53/0.40 % Maximum resident set size: 6424 pages
% 0.53/0.40
% 0.53/0.40 % -------------------------------------------------
% 0.53/0.40 % User time : 0.101 s
% 0.53/0.40 % System time : 0.018 s
% 0.53/0.40 % Total time : 0.119 s
% 0.53/0.40 % Maximum resident set size: 6144 pages
% 0.53/0.40 % E exiting
%------------------------------------------------------------------------------