%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP092^1 : 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 : n013.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 08:04:20 AM UTC 2026
% Result : Theorem 2.57s 0.74s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 186 ( 13 ~; 3 |; 1 &; 168 @)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 1 ^; 47 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
list_P1467822637od_a_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
product_prod_a_a: $tType ).
thf(decl_26,type,
kurato1072996284sing_a: list_P1467822637od_a_a > $o ).
thf(decl_32,type,
append1574001858od_a_a: list_P1467822637od_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(decl_68,type,
cons_P1921020637od_a_a: product_prod_a_a > list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(decl_145,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(decl_173,type,
e: product_prod_a_a ).
thf(decl_174,type,
es: list_P1467822637od_a_a ).
thf(decl_186,type,
esk9_1: list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(decl_187,type,
esk10_1: list_P1467822637od_a_a > a ).
thf(decl_188,type,
esk11_1: list_P1467822637od_a_a > a ).
thf(decl_189,type,
esk12_1: list_P1467822637od_a_a > list_P1467822637od_a_a ).
thf(decl_615,type,
esk424_0: list_P1467822637od_a_a ).
thf(decl_616,type,
esk425_0: a ).
thf(decl_617,type,
esk426_0: a ).
thf(decl_618,type,
esk427_0: list_P1467822637od_a_a ).
thf(conj_0,conjecture,
! [X790: list_P1467822637od_a_a,X1235: a,X274: a,X792: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X790 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X1235 @ X274 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X274 @ X1235 ) @ X792 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bNzCnQYl0c/E---3.1_2576014.p',conj_0) ).
thf(fact_3_progressing__def,axiom,
( kurato1072996284sing_a
= ( ^ [X11: list_P1467822637od_a_a] :
! [X12: list_P1467822637od_a_a,X13: a,X14: a,X15: list_P1467822637od_a_a] :
( X11
!= ( append1574001858od_a_a @ X12 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X13 @ X14 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X14 @ X13 ) @ X15 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bNzCnQYl0c/E---3.1_2576014.p',fact_3_progressing__def) ).
thf(fact_46_append__Cons,axiom,
! [X152: product_prod_a_a,X153: list_P1467822637od_a_a,X154: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X152 @ X153 ) @ X154 )
= ( cons_P1921020637od_a_a @ X152 @ ( append1574001858od_a_a @ X153 @ X154 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.bNzCnQYl0c/E---3.1_2576014.p',fact_46_append__Cons) ).
thf(fact_0_assms,axiom,
kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ),
file('/export/starexec/sandbox2/tmp/tmp.bNzCnQYl0c/E---3.1_2576014.p',fact_0_assms) ).
thf(c_0_4,negated_conjecture,
~ ! [X790: list_P1467822637od_a_a,X1235: a,X274: a,X792: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X790 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X1235 @ X274 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X274 @ X1235 ) @ X792 ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,plain,
! [X2807: list_P1467822637od_a_a] :
( ( kurato1072996284sing_a @ X2807 )
<=> ! [X12: list_P1467822637od_a_a,X13: a,X14: a,X15: list_P1467822637od_a_a] :
( X2807
!= ( append1574001858od_a_a @ X12 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X13 @ X14 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X14 @ X13 ) @ X15 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_3_progressing__def])])]) ).
thf(c_0_6,negated_conjecture,
~ ! [X790: list_P1467822637od_a_a,X1235: a,X274: a,X792: list_P1467822637od_a_a] :
( es
!= ( append1574001858od_a_a @ X790 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X1235 @ X274 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X274 @ X1235 ) @ X792 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X2833: list_P1467822637od_a_a,X2834: list_P1467822637od_a_a,X2835: a,X2836: a,X2837: list_P1467822637od_a_a,X2838: list_P1467822637od_a_a] :
( ( ~ ( kurato1072996284sing_a @ X2833 )
| ( X2833
!= ( append1574001858od_a_a @ X2834 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2835 @ X2836 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X2836 @ X2835 ) @ X2837 ) ) ) ) )
& ( ( X2838
= ( append1574001858od_a_a @ ( esk9_1 @ X2838 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ ( esk10_1 @ X2838 ) @ ( esk11_1 @ X2838 ) ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ ( esk11_1 @ X2838 ) @ ( esk10_1 @ X2838 ) ) @ ( esk12_1 @ X2838 ) ) ) ) )
| ( kurato1072996284sing_a @ X2838 ) ) ),
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_5])])])])])]) ).
thf(c_0_8,plain,
! [X2996: product_prod_a_a,X2997: list_P1467822637od_a_a,X2998: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X2996 @ X2997 ) @ X2998 )
= ( cons_P1921020637od_a_a @ X2996 @ ( append1574001858od_a_a @ X2997 @ X2998 ) ) ),
inference(variable_rename,[status(thm)],[fact_46_append__Cons]) ).
thf(c_0_9,negated_conjecture,
( es
= ( append1574001858od_a_a @ esk424_0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ esk425_0 @ esk426_0 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ esk426_0 @ esk425_0 ) @ esk427_0 ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_10,plain,
! [X11: list_P1467822637od_a_a,X12: list_P1467822637od_a_a,X13: a,X14: a,X15: list_P1467822637od_a_a] :
( ~ ( kurato1072996284sing_a @ X11 )
| ( X11
!= ( append1574001858od_a_a @ X12 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X13 @ X14 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X14 @ X13 ) @ X15 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,plain,
! [X3: product_prod_a_a,X11: list_P1467822637od_a_a,X12: list_P1467822637od_a_a] :
( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X3 @ X11 ) @ X12 )
= ( cons_P1921020637od_a_a @ X3 @ ( append1574001858od_a_a @ X11 @ X12 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
( es
= ( append1574001858od_a_a @ esk424_0 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ esk425_0 @ esk426_0 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ esk426_0 @ esk425_0 ) @ esk427_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X11: list_P1467822637od_a_a,X14: a,X13: a,X12: list_P1467822637od_a_a] :
~ ( kurato1072996284sing_a @ ( append1574001858od_a_a @ X11 @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X13 @ X14 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ X14 @ X13 ) @ X12 ) ) ) ),
inference(er,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X3: product_prod_a_a] :
( ( append1574001858od_a_a @ ( cons_P1921020637od_a_a @ X3 @ esk424_0 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ esk425_0 @ esk426_0 ) @ ( cons_P1921020637od_a_a @ ( product_Pair_a_a @ esk426_0 @ esk425_0 ) @ esk427_0 ) ) )
= ( cons_P1921020637od_a_a @ X3 @ es ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,plain,
kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ e @ es ),
inference(split_conjunct,[status(thm)],[fact_0_assms]) ).
thf(c_0_16,negated_conjecture,
! [X3: product_prod_a_a] :
~ ( kurato1072996284sing_a @ ( cons_P1921020637od_a_a @ X3 @ es ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,plain,
$false,
inference(sr,[status(thm)],[c_0_15,c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP092^1 : 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 : n013.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 19:51:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.32 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.bNzCnQYl0c/E---3.1_2576014.p
% 2.57/0.74 % Version: 3.5.1-ho
% 2.57/0.74 % Preprocessing class: HSLMSMSSSSMNHFA.
% 2.57/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.57/0.74 % Starting lpo5_fix with 1500s (5) cores
% 2.57/0.74 % Starting new_bool_3 with 300s (1) cores
% 2.57/0.74 % Starting new_bool_1 with 300s (1) cores
% 2.57/0.74 % Starting new_bool_2 with 300s (1) cores
% 2.57/0.74 % lpo5_fix with pid 2576056 completed with status 0
% 2.57/0.74 % Result found by lpo5_fix
% 2.57/0.74 % Preprocessing class: HSLMSMSSSSMNHFA.
% 2.57/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.57/0.74 % Starting lpo5_fix with 1500s (5) cores
% 2.57/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.57/0.74 % No SInE strategy applied
% 2.57/0.74 % Search class: HGHSM-FSLS31-DHFFFSBN
% 2.57/0.74 % partial match(1): HGHSM-FSLM31-DHFFFSBN
% 2.57/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.57/0.74 % Starting SubtermCWHack with 136s (1) cores
% 2.57/0.74 % Starting lpo5_fix with 151s (1) cores
% 2.57/0.74 % Starting new_bool_6 with 136s (1) cores
% 2.57/0.74 % Starting lpo8_s with 136s (1) cores
% 2.57/0.74 % Starting lpo1_lambda_fix with 136s (1) cores
% 2.57/0.74 % lpo5_fix with pid 2576078 completed with status 0
% 2.57/0.74 % Result found by lpo5_fix
% 2.57/0.74 % Preprocessing class: HSLMSMSSSSMNHFA.
% 2.57/0.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.57/0.74 % Starting lpo5_fix with 1500s (5) cores
% 2.57/0.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.57/0.74 % No SInE strategy applied
% 2.57/0.74 % Search class: HGHSM-FSLS31-DHFFFSBN
% 2.57/0.74 % partial match(1): HGHSM-FSLM31-DHFFFSBN
% 2.57/0.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.57/0.74 % Starting SubtermCWHack with 136s (1) cores
% 2.57/0.74 % Starting lpo5_fix with 151s (1) cores
% 2.57/0.74 % Preprocessing time : 0.021 s
% 2.57/0.74
% 2.57/0.74 % Proof found!
% 2.57/0.74 % SZS status Theorem
% 2.57/0.74 % SZS output start CNFRefutation
% See solution above
% 2.57/0.74 % Parsed axioms : 566
% 2.57/0.74 % Removed by relevancy pruning/SinE : 0
% 2.57/0.74 % Initial clauses : 1155
% 2.57/0.74 % Removed in clause preprocessing : 249
% 2.57/0.74 % Initial clauses in saturation : 906
% 2.57/0.74 % Processed clauses : 1038
% 2.57/0.74 % ...of these trivial : 18
% 2.57/0.74 % ...subsumed : 102
% 2.57/0.74 % ...remaining for further processing : 918
% 2.57/0.74 % Other redundant clauses eliminated : 644
% 2.57/0.74 % Clauses deleted for lack of memory : 0
% 2.57/0.74 % Backward-subsumed : 3
% 2.57/0.74 % Backward-rewritten : 1
% 2.57/0.74 % Generated clauses : 3993
% 2.57/0.74 % ...of the previous two non-redundant : 3510
% 2.57/0.74 % ...aggressively subsumed : 0
% 2.57/0.74 % Contextual simplify-reflections : 1
% 2.57/0.74 % Paramodulations : 3256
% 2.57/0.74 % Factorizations : 0
% 2.57/0.74 % NegExts : 0
% 2.57/0.74 % Equation resolutions : 724
% 2.57/0.74 % Disequality decompositions : 0
% 2.57/0.74 % Total rewrite steps : 281
% 2.57/0.74 % ...of those cached : 143
% 2.57/0.74 % Propositional unsat checks : 0
% 2.57/0.74 % Propositional check models : 0
% 2.57/0.74 % Propositional check unsatisfiable : 0
% 2.57/0.74 % Propositional clauses : 0
% 2.57/0.74 % Propositional clauses after purity: 0
% 2.57/0.74 % Propositional unsat core size : 0
% 2.57/0.74 % Propositional preprocessing time : 0.000
% 2.57/0.74 % Propositional encoding time : 0.000
% 2.57/0.74 % Propositional solver time : 0.000
% 2.57/0.74 % Success case prop preproc time : 0.000
% 2.57/0.74 % Success case prop encoding time : 0.000
% 2.57/0.74 % Success case prop solver time : 0.000
% 2.57/0.74 % Current number of processed clauses : 640
% 2.57/0.74 % Positive orientable unit clauses : 71
% 2.57/0.74 % Positive unorientable unit clauses: 21
% 2.57/0.74 % Negative unit clauses : 31
% 2.57/0.74 % Non-unit-clauses : 517
% 2.57/0.74 % Current number of unprocessed clauses: 3371
% 2.57/0.74 % ...number of literals in the above : 10903
% 2.57/0.74 % Current number of archived formulas : 0
% 2.57/0.74 % Current number of archived clauses : 5
% 2.57/0.74 % Clause-clause subsumption calls (NU) : 135613
% 2.57/0.74 % Rec. Clause-clause subsumption calls : 49626
% 2.57/0.74 % Non-unit clause-clause subsumptions : 76
% 2.57/0.74 % Unit Clause-clause subsumption calls : 4215
% 2.57/0.74 % Rewrite failures with RHS unbound : 0
% 2.57/0.74 % BW rewrite match attempts : 8
% 2.57/0.74 % BW rewrite match successes : 1
% 2.57/0.74 % Condensation attempts : 1038
% 2.57/0.74 % Condensation successes : 0
% 2.57/0.74 % Termbank termtop insertions : 168281
% 2.57/0.74 % Search garbage collected termcells : 23533
% 2.57/0.74
% 2.57/0.74 % -------------------------------------------------
% 2.57/0.74 % User time : 0.355 s
% 2.57/0.74 % System time : 0.021 s
% 2.57/0.74 % Total time : 0.375 s
% 2.57/0.74 % Maximum resident set size: 9596 pages
% 2.57/0.74
% 2.57/0.74 % -------------------------------------------------
% 2.57/0.74 % User time : 1.397 s
% 2.57/0.74 % System time : 0.093 s
% 2.57/0.74 % Total time : 1.490 s
% 2.57/0.74 % Maximum resident set size: 6400 pages
% 2.57/0.74 % E exiting
%------------------------------------------------------------------------------