%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP180^1 : 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 : n002.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 08:04:36 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 3 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 210 ( 11 ~; 7 |; 0 &; 190 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 0 ^; 24 !; 2 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
standard_Constant_V: $tType ).
thf(decl_sort2,type,
product_prod_V_V: $tType ).
thf(decl_sort3,type,
v: $tType ).
thf(decl_sort4,type,
set_Product_prod_V_V: $tType ).
thf(decl_sort5,type,
v2: $tType ).
thf(decl_sort6,type,
set_V: $tType ).
thf(decl_sort7,type,
labele2115946735nt_V_V: $tType ).
thf(decl_28,type,
bNF_Gr_V_V2: set_V > ( v > v ) > set_Product_prod_V_V ).
thf(decl_34,type,
standard_S_Const_V: v2 > standard_Constant_V ).
thf(decl_39,type,
getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V ).
thf(decl_48,type,
graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).
thf(decl_61,type,
labele1134902411nt_V_V: labele2115946735nt_V_V > set_V ).
thf(decl_65,type,
map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).
thf(decl_105,type,
product_Pair_V_V2: v > v > product_prod_V_V ).
thf(decl_111,type,
id_on_V2: set_V > set_Product_prod_V_V ).
thf(decl_150,type,
member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o ).
thf(decl_154,type,
g: labele2115946735nt_V_V ).
thf(decl_156,type,
h: v > v ).
thf(decl_157,type,
m: v2 > v ).
thf(decl_159,type,
xa: v2 ).
thf(decl_160,type,
y: v2 ).
thf(decl_162,type,
esk2_1: product_prod_V_V > v ).
thf(decl_163,type,
esk3_1: product_prod_V_V > v ).
thf(fact_38_getRel__subgraph,axiom,
! [X27: v,X28: v,X29: standard_Constant_V,X30: labele2115946735nt_V_V,X67: labele2115946735nt_V_V] :
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X27 @ X28 ) @ ( getRel1432786916nt_V_V @ X29 @ X30 ) )
=> ( ( graph_1808119_V_V_V @ X30 @ X67 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X30 ) ) )
=> ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X27 @ X28 ) @ ( getRel1432786916nt_V_V @ X29 @ X67 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.DYTsIfq1j6/E---3.1_1790231.p',fact_38_getRel__subgraph) ).
thf(fact_22_surj__pair,axiom,
! [X34: product_prod_V_V] :
? [X1: v,X35: v] :
( X34
= ( product_Pair_V_V2 @ X1 @ X35 ) ),
file('/export/starexec/sandbox2/tmp/tmp.DYTsIfq1j6/E---3.1_1790231.p',fact_22_surj__pair) ).
thf(conj_0,conjecture,
member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ),
file('/export/starexec/sandbox2/tmp/tmp.DYTsIfq1j6/E---3.1_1790231.p',conj_0) ).
thf(fact_8_h_I3_J,axiom,
graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.DYTsIfq1j6/E---3.1_1790231.p',fact_8_h_I3_J) ).
thf(fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
file('/export/starexec/sandbox2/tmp/tmp.DYTsIfq1j6/E---3.1_1790231.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(c_0_5,plain,
! [X933: v,X934: v,X935: standard_Constant_V,X936: labele2115946735nt_V_V,X937: labele2115946735nt_V_V] :
( ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X933 @ X934 ) @ ( getRel1432786916nt_V_V @ X935 @ X936 ) )
| ~ ( graph_1808119_V_V_V @ X936 @ X937 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X936 ) ) )
| ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X933 @ X934 ) @ ( getRel1432786916nt_V_V @ X935 @ X937 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_38_getRel__subgraph])])]) ).
thf(c_0_6,plain,
! [X848: product_prod_V_V] :
( X848
= ( product_Pair_V_V2 @ ( esk2_1 @ X848 ) @ ( esk3_1 @ X848 ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_22_surj__pair])]) ).
thf(c_0_7,negated_conjecture,
~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_8,plain,
! [X1: v,X4: v,X8: standard_Constant_V,X67: labele2115946735nt_V_V,X30: labele2115946735nt_V_V] :
( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X1 @ X4 ) @ ( getRel1432786916nt_V_V @ X8 @ X67 ) )
| ~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X1 @ X4 ) @ ( getRel1432786916nt_V_V @ X8 @ X30 ) )
| ~ ( graph_1808119_V_V_V @ X30 @ X67 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X30 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,plain,
! [X9: product_prod_V_V] :
( X9
= ( product_Pair_V_V2 @ ( esk2_1 @ X9 ) @ ( esk3_1 @ X9 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X8: standard_Constant_V,X30: labele2115946735nt_V_V,X9: product_prod_V_V,X67: labele2115946735nt_V_V] :
( ( member2015049524od_V_V @ X9 @ ( getRel1432786916nt_V_V @ X8 @ X30 ) )
| ~ ( graph_1808119_V_V_V @ X67 @ X30 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X67 ) ) )
| ~ ( member2015049524od_V_V @ X9 @ ( getRel1432786916nt_V_V @ X8 @ X67 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,plain,
graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ),
inference(split_conjunct,[status(thm)],[fact_8_h_I3_J]) ).
thf(c_0_13,negated_conjecture,
~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X9: product_prod_V_V,X8: standard_Constant_V] :
( ( member2015049524od_V_V @ X9 @ ( getRel1432786916nt_V_V @ X8 @ g ) )
| ~ ( member2015049524od_V_V @ X9 @ ( getRel1432786916nt_V_V @ X8 @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,plain,
member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ),
inference(split_conjunct,[status(thm)],[fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062]) ).
thf(c_0_16,negated_conjecture,
~ ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP180^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:09:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.30 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.DYTsIfq1j6/E---3.1_1790231.p
% 0.21/0.34 % Version: 3.5.1-ho
% 0.21/0.34 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.34 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.34 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.34 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.34 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.34 % Starting post_as_ho6 with 300s (1) cores
% 0.21/0.34 % post_as_ho6 with pid 1790248 completed with status 0
% 0.21/0.34 % Result found by post_as_ho6
% 0.21/0.34 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.34 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.34 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.34 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.34 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.34 % Starting post_as_ho6 with 300s (1) cores
% 0.21/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 0.21/0.34 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.21/0.34 % Search class: HGHSM-FFMM31-MHFFFSBN
% 0.21/0.34 % partial match(2): HGHSM-FSLM31-MHFFFSBN
% 0.21/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.34 % SubtermCWHack with pid 1790250 completed with status 0
% 0.21/0.34 % Result found by SubtermCWHack
% 0.21/0.34 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.34 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.34 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.34 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.34 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.34 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.34 % Starting post_as_ho6 with 300s (1) cores
% 0.21/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true))
% 0.21/0.34 % SinE strategy is GSinE(CountFormulas,,true,2.0,0,3,20000,1.0,true)
% 0.21/0.34 % Search class: HGHSM-FFMM31-MHFFFSBN
% 0.21/0.34 % partial match(2): HGHSM-FSLM31-MHFFFSBN
% 0.21/0.34 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.34 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.34 % Preprocessing time : 0.002 s
% 0.21/0.34
% 0.21/0.34 % Proof found!
% 0.21/0.34 % SZS status Theorem
% 0.21/0.34 % SZS output start CNFRefutation
% See solution above
% 0.21/0.34 % Parsed axioms : 537
% 0.21/0.34 % Removed by relevancy pruning/SinE : 473
% 0.21/0.34 % Initial clauses : 83
% 0.21/0.34 % Removed in clause preprocessing : 3
% 0.21/0.34 % Initial clauses in saturation : 80
% 0.21/0.34 % Processed clauses : 280
% 0.21/0.34 % ...of these trivial : 11
% 0.21/0.34 % ...subsumed : 140
% 0.21/0.34 % ...remaining for further processing : 129
% 0.21/0.34 % Other redundant clauses eliminated : 31
% 0.21/0.34 % Clauses deleted for lack of memory : 0
% 0.21/0.34 % Backward-subsumed : 1
% 0.21/0.34 % Backward-rewritten : 10
% 0.21/0.34 % Generated clauses : 449
% 0.21/0.34 % ...of the previous two non-redundant : 340
% 0.21/0.34 % ...aggressively subsumed : 0
% 0.21/0.34 % Contextual simplify-reflections : 0
% 0.21/0.34 % Paramodulations : 415
% 0.21/0.34 % Factorizations : 0
% 0.21/0.34 % NegExts : 0
% 0.21/0.34 % Equation resolutions : 34
% 0.21/0.34 % Disequality decompositions : 0
% 0.21/0.34 % Total rewrite steps : 202
% 0.21/0.34 % ...of those cached : 146
% 0.21/0.34 % Propositional unsat checks : 0
% 0.21/0.34 % Propositional check models : 0
% 0.21/0.34 % Propositional check unsatisfiable : 0
% 0.21/0.34 % Propositional clauses : 0
% 0.21/0.34 % Propositional clauses after purity: 0
% 0.21/0.34 % Propositional unsat core size : 0
% 0.21/0.34 % Propositional preprocessing time : 0.000
% 0.21/0.34 % Propositional encoding time : 0.000
% 0.21/0.34 % Propositional solver time : 0.000
% 0.21/0.34 % Success case prop preproc time : 0.000
% 0.21/0.34 % Success case prop encoding time : 0.000
% 0.21/0.34 % Success case prop solver time : 0.000
% 0.21/0.34 % Current number of processed clauses : 109
% 0.21/0.34 % Positive orientable unit clauses : 27
% 0.21/0.34 % Positive unorientable unit clauses: 0
% 0.21/0.34 % Negative unit clauses : 3
% 0.21/0.34 % Non-unit-clauses : 79
% 0.21/0.34 % Current number of unprocessed clauses: 112
% 0.21/0.34 % ...number of literals in the above : 333
% 0.21/0.34 % Current number of archived formulas : 0
% 0.21/0.34 % Current number of archived clauses : 11
% 0.21/0.34 % Clause-clause subsumption calls (NU) : 1059
% 0.21/0.34 % Rec. Clause-clause subsumption calls : 1015
% 0.21/0.34 % Non-unit clause-clause subsumptions : 108
% 0.21/0.34 % Unit Clause-clause subsumption calls : 29
% 0.21/0.34 % Rewrite failures with RHS unbound : 0
% 0.21/0.34 % BW rewrite match attempts : 10
% 0.21/0.34 % BW rewrite match successes : 8
% 0.21/0.34 % Condensation attempts : 0
% 0.21/0.34 % Condensation successes : 0
% 0.21/0.34 % Termbank termtop insertions : 17251
% 0.21/0.34 % Search garbage collected termcells : 4609
% 0.21/0.34
% 0.21/0.34 % -------------------------------------------------
% 0.21/0.34 % User time : 0.019 s
% 0.21/0.34 % System time : 0.003 s
% 0.21/0.34 % Total time : 0.022 s
% 0.21/0.34 % Maximum resident set size: 5132 pages
% 0.21/0.34
% 0.21/0.34 % -------------------------------------------------
% 0.21/0.34 % User time : 0.027 s
% 0.21/0.34 % System time : 0.006 s
% 0.21/0.34 % Total time : 0.033 s
% 0.21/0.34 % Maximum resident set size: 5888 pages
% 0.21/0.34 % E exiting
%------------------------------------------------------------------------------