%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 07:47:24 AM UTC 2026
% Result : Theorem 0.25s 0.34s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 33 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 290 ( 10 ~; 10 |; 1 &; 266 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
lst: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_23,type,
ap: lst > lst > lst ).
thf(decl_24,type,
cns: a > lst > lst ).
thf(decl_25,type,
nl: lst ).
thf(decl_26,type,
xs: lst ).
thf(decl_27,type,
esk1_0: lst ).
thf(decl_28,type,
esk2_0: lst ).
thf(decl_29,type,
esk3_0: a ).
thf(decl_30,type,
esk4_0: lst ).
thf(decl_31,type,
esk5_0: lst ).
thf(decl_32,type,
esk6_0: lst ).
thf(decl_33,type,
esk7_0: lst ).
thf(decl_34,type,
esk8_0: lst ).
thf(fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093,axiom,
! [X1: lst] :
( ! [X2: lst,X3: lst] :
( ( ap @ nl @ ( ap @ X2 @ X3 ) )
= ( ap @ ( ap @ nl @ X2 ) @ X3 ) )
=> ( ! [X4: a,X5: lst] :
( ! [X6: lst,X7: lst] :
( ( ap @ X5 @ ( ap @ X6 @ X7 ) )
= ( ap @ ( ap @ X5 @ X6 ) @ X7 ) )
=> ! [X2: lst,X3: lst] :
( ( ap @ ( cns @ X4 @ X5 ) @ ( ap @ X2 @ X3 ) )
= ( ap @ ( ap @ ( cns @ X4 @ X5 ) @ X2 ) @ X3 ) ) )
=> ! [X6: lst,X7: lst] :
( ( ap @ X1 @ ( ap @ X6 @ X7 ) )
= ( ap @ ( ap @ X1 @ X6 ) @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tYovnmHFpT/E---3.1_1637904.p',fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093) ).
thf(fact_2p_Osimps_I1_J,axiom,
! [X8: lst] :
( ( ap @ nl @ X8 )
= X8 ),
file('/export/starexec/sandbox/tmp/tmp.tYovnmHFpT/E---3.1_1637904.p',fact_2p_Osimps_I1_J) ).
thf(fact_1p_Osimps_I2_J,axiom,
! [X8: lst,X9: lst,X10: a] :
( ( ap @ ( cns @ X10 @ X9 ) @ X8 )
= ( cns @ X10 @ ( ap @ X9 @ X8 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tYovnmHFpT/E---3.1_1637904.p',fact_1p_Osimps_I2_J) ).
thf(conj_0,conjecture,
! [X2: lst,X3: lst] :
( ( ap @ xs @ ( ap @ X2 @ X3 ) )
= ( ap @ ( ap @ xs @ X2 ) @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.tYovnmHFpT/E---3.1_1637904.p',conj_0) ).
thf(c_0_4,plain,
! [X32: lst,X33: lst,X36: lst,X37: lst,X38: lst] :
( ( ( ( ap @ esk4_0 @ ( ap @ X32 @ X33 ) )
= ( ap @ ( ap @ esk4_0 @ X32 ) @ X33 ) )
| ( ( ap @ X36 @ ( ap @ X37 @ X38 ) )
= ( ap @ ( ap @ X36 @ X37 ) @ X38 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) ) )
& ( ( ( ap @ ( cns @ esk3_0 @ esk4_0 ) @ ( ap @ esk5_0 @ esk6_0 ) )
!= ( ap @ ( ap @ ( cns @ esk3_0 @ esk4_0 ) @ esk5_0 ) @ esk6_0 ) )
| ( ( ap @ X36 @ ( ap @ X37 @ X38 ) )
= ( ap @ ( ap @ X36 @ X37 ) @ X38 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) ) ) ),
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)],[fact_0_lst_Oinduct_091where_AP_A_061_A_C_Fxs_O_AALL_Ays_Azs_O_Aap_Axs_A_Iap_Ays_Azs_J_A_061_Aap_A_Iap_Axs_Ays_J_Azs_C_093])])])])])])]) ).
thf(c_0_5,plain,
! [X42: lst] :
( ( ap @ nl @ X42 )
= X42 ),
inference(variable_rename,[status(thm)],[fact_2p_Osimps_I1_J]) ).
thf(c_0_6,plain,
! [X1: lst,X2: lst,X3: lst,X5: lst,X6: lst] :
( ( ( ap @ esk4_0 @ ( ap @ X1 @ X2 ) )
= ( ap @ ( ap @ esk4_0 @ X1 ) @ X2 ) )
| ( ( ap @ X3 @ ( ap @ X5 @ X6 ) )
= ( ap @ ( ap @ X3 @ X5 ) @ X6 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X1: lst] :
( ( ap @ nl @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,plain,
! [X39: lst,X40: lst,X41: a] :
( ( ap @ ( cns @ X41 @ X40 ) @ X39 )
= ( cns @ X41 @ ( ap @ X40 @ X39 ) ) ),
inference(variable_rename,[status(thm)],[fact_1p_Osimps_I2_J]) ).
thf(c_0_9,plain,
! [X1: lst,X2: lst,X3: lst,X5: lst,X6: lst] :
( ( ( ap @ ( ap @ esk4_0 @ X1 ) @ X2 )
= ( ap @ esk4_0 @ ( ap @ X1 @ X2 ) ) )
| ( ( ap @ ( ap @ X3 @ X5 ) @ X6 )
= ( ap @ X3 @ ( ap @ X5 @ X6 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7]),c_0_7])]) ).
thf(c_0_10,negated_conjecture,
~ ! [X2: lst,X3: lst] :
( ( ap @ xs @ ( ap @ X2 @ X3 ) )
= ( ap @ ( ap @ xs @ X2 ) @ X3 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_11,plain,
! [X1: lst,X2: lst,X3: lst] :
( ( ( ap @ X1 @ ( ap @ X2 @ X3 ) )
= ( ap @ ( ap @ X1 @ X2 ) @ X3 ) )
| ( ( ap @ ( cns @ esk3_0 @ esk4_0 ) @ ( ap @ esk5_0 @ esk6_0 ) )
!= ( ap @ ( ap @ ( cns @ esk3_0 @ esk4_0 ) @ esk5_0 ) @ esk6_0 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_12,plain,
! [X1: lst,X4: a,X2: lst] :
( ( ap @ ( cns @ X4 @ X1 ) @ X2 )
= ( cns @ X4 @ ( ap @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
! [X1: lst,X2: lst] :
( ( ap @ ( ap @ esk4_0 @ X1 ) @ X2 )
= ( ap @ esk4_0 @ ( ap @ X1 @ X2 ) ) ),
inference(ef,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( ap @ xs @ ( ap @ esk7_0 @ esk8_0 ) )
!= ( ap @ ( ap @ xs @ esk7_0 ) @ esk8_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
thf(c_0_15,plain,
! [X1: lst,X2: lst,X3: lst] :
( ( ( ap @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ X1 @ ( ap @ X2 @ X3 ) ) )
| ( ( ap @ ( ap @ ( cns @ esk3_0 @ esk4_0 ) @ esk5_0 ) @ esk6_0 )
!= ( ap @ ( cns @ esk3_0 @ esk4_0 ) @ ( ap @ esk5_0 @ esk6_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_7]),c_0_7])]) ).
thf(c_0_16,plain,
! [X1: lst,X4: a,X2: lst] :
( ( ap @ ( ap @ ( cns @ X4 @ esk4_0 ) @ X1 ) @ X2 )
= ( ap @ ( cns @ X4 @ esk4_0 ) @ ( ap @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_12]),c_0_12]) ).
thf(c_0_17,negated_conjecture,
( ( ap @ xs @ ( ap @ esk7_0 @ esk8_0 ) )
!= ( ap @ ( ap @ xs @ esk7_0 ) @ esk8_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,plain,
! [X1: lst,X2: lst,X3: lst] :
( ( ap @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ X1 @ ( ap @ X2 @ X3 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT056^1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n004.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 17:58:07 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.30 Running higher-order theorem proving
% 0.25/0.31 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.tYovnmHFpT/E---3.1_1637904.p
% 0.25/0.34 % Version: 3.5.1-ho
% 0.25/0.34 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.25/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.34 % Starting full_lambda_5 with 300s (1) cores
% 0.25/0.34 % Starting new_ho_10_unif with 300s (1) cores
% 0.25/0.34 % new_ho_10 with pid 1637921 completed with status 0
% 0.25/0.34 % Result found by new_ho_10
% 0.25/0.34 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.25/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.34 % No SInE strategy applied
% 0.25/0.34 % Search class: HGUPS-FFSF22-MFFFFFNN
% 0.25/0.34 % partial match(2): FUUPS-FFSF22-MFFFFFNN
% 0.25/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.34 % Starting new_ho_10 with 151s (1) cores
% 0.25/0.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.25/0.34 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.34 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.34 % new_bool_3 with pid 1637929 completed with status 0
% 0.25/0.34 % Result found by new_bool_3
% 0.25/0.34 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.25/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.34 % Starting new_ho_10 with 1500s (5) cores
% 0.25/0.34 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.34 % No SInE strategy applied
% 0.25/0.34 % Search class: HGUPS-FFSF22-MFFFFFNN
% 0.25/0.34 % partial match(2): FUUPS-FFSF22-MFFFFFNN
% 0.25/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.34 % Starting new_ho_10 with 151s (1) cores
% 0.25/0.34 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.25/0.34 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.34 % Preprocessing time : 0.001 s
% 0.25/0.34 % Presaturation interreduction done
% 0.25/0.34
% 0.25/0.34 % Proof found!
% 0.25/0.34 % SZS status Theorem
% 0.25/0.34 % SZS output start CNFRefutation
% See solution above
% 0.25/0.34 % Parsed axioms : 10
% 0.25/0.34 % Removed by relevancy pruning/SinE : 0
% 0.25/0.34 % Initial clauses : 11
% 0.25/0.34 % Removed in clause preprocessing : 6
% 0.25/0.34 % Initial clauses in saturation : 5
% 0.25/0.34 % Processed clauses : 16
% 0.25/0.34 % ...of these trivial : 0
% 0.25/0.34 % ...subsumed : 0
% 0.25/0.34 % ...remaining for further processing : 16
% 0.25/0.34 % Other redundant clauses eliminated : 0
% 0.25/0.34 % Clauses deleted for lack of memory : 0
% 0.25/0.34 % Backward-subsumed : 1
% 0.25/0.34 % Backward-rewritten : 3
% 0.25/0.34 % Generated clauses : 25
% 0.25/0.34 % ...of the previous two non-redundant : 14
% 0.25/0.34 % ...aggressively subsumed : 0
% 0.25/0.34 % Contextual simplify-reflections : 0
% 0.25/0.34 % Paramodulations : 21
% 0.25/0.34 % Factorizations : 2
% 0.25/0.34 % NegExts : 0
% 0.25/0.34 % Equation resolutions : 0
% 0.25/0.34 % Disequality decompositions : 0
% 0.25/0.34 % Total rewrite steps : 27
% 0.25/0.34 % ...of those cached : 3
% 0.25/0.34 % Propositional unsat checks : 0
% 0.25/0.34 % Propositional check models : 0
% 0.25/0.34 % Propositional check unsatisfiable : 0
% 0.25/0.34 % Propositional clauses : 0
% 0.25/0.34 % Propositional clauses after purity: 0
% 0.25/0.34 % Propositional unsat core size : 0
% 0.25/0.34 % Propositional preprocessing time : 0.000
% 0.25/0.34 % Propositional encoding time : 0.000
% 0.25/0.34 % Propositional solver time : 0.000
% 0.25/0.34 % Success case prop preproc time : 0.000
% 0.25/0.34 % Success case prop encoding time : 0.000
% 0.25/0.34 % Success case prop solver time : 0.000
% 0.25/0.34 % Current number of processed clauses : 7
% 0.25/0.34 % Positive orientable unit clauses : 7
% 0.25/0.34 % Positive unorientable unit clauses: 0
% 0.25/0.34 % Negative unit clauses : 0
% 0.25/0.34 % Non-unit-clauses : 0
% 0.25/0.34 % Current number of unprocessed clauses: 6
% 0.25/0.34 % ...number of literals in the above : 12
% 0.25/0.34 % Current number of archived formulas : 0
% 0.25/0.34 % Current number of archived clauses : 9
% 0.25/0.34 % Clause-clause subsumption calls (NU) : 1
% 0.25/0.34 % Rec. Clause-clause subsumption calls : 1
% 0.25/0.34 % Non-unit clause-clause subsumptions : 0
% 0.25/0.34 % Unit Clause-clause subsumption calls : 1
% 0.25/0.34 % Rewrite failures with RHS unbound : 0
% 0.25/0.34 % BW rewrite match attempts : 5
% 0.25/0.34 % BW rewrite match successes : 4
% 0.25/0.34 % Condensation attempts : 0
% 0.25/0.34 % Condensation successes : 0
% 0.25/0.34 % Termbank termtop insertions : 2009
% 0.25/0.34 % Search garbage collected termcells : 179
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.005 s
% 0.25/0.34 % System time : 0.003 s
% 0.25/0.34 % Total time : 0.008 s
% 0.25/0.34 % Maximum resident set size: 3640 pages
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.020 s
% 0.25/0.34 % System time : 0.013 s
% 0.25/0.34 % Total time : 0.033 s
% 0.25/0.34 % Maximum resident set size: 4864 pages
% 0.25/0.34 % E exiting
%------------------------------------------------------------------------------