%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : DAT056^2 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 0.10s 0.25s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 384 ( 13 ~; 15 |; 1 &; 352 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 14 ^; 33 !; 0 ?; 47 :)
% 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_2: lst > ( lst > $o ) > a ).
thf(decl_30,type,
esk4_2: lst > ( lst > $o ) > lst ).
thf(conj_0,conjecture,
! [X8: lst,X9: lst] :
( ( ap @ xs @ ( ap @ X8 @ X9 ) )
= ( ap @ ( ap @ xs @ X8 ) @ X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.txZLUfnofr/E---3.1_1100775.p',conj_0) ).
thf(fact_0_lst_Oinduct,axiom,
! [X1: lst,X2: lst > $o] :
( ( X2 @ nl )
=> ( ! [X3: a,X4: lst] :
( ( X2 @ X4 )
=> ( X2 @ ( cns @ X3 @ X4 ) ) )
=> ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.txZLUfnofr/E---3.1_1100775.p',fact_0_lst_Oinduct) ).
thf(fact_2p_Osimps_I1_J,axiom,
! [X5: lst] :
( ( ap @ nl @ X5 )
= X5 ),
file('/export/starexec/sandbox2/tmp/tmp.txZLUfnofr/E---3.1_1100775.p',fact_2p_Osimps_I1_J) ).
thf(fact_1p_Osimps_I2_J,axiom,
! [X5: lst,X6: lst,X7: a] :
( ( ap @ ( cns @ X7 @ X6 ) @ X5 )
= ( cns @ X7 @ ( ap @ X6 @ X5 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.txZLUfnofr/E---3.1_1100775.p',fact_1p_Osimps_I2_J) ).
thf(c_0_4,negated_conjecture,
~ ! [X8: lst,X9: lst] :
( ( ap @ xs @ ( ap @ X8 @ X9 ) )
= ( ap @ ( ap @ xs @ X8 ) @ X9 ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,plain,
! [X26: lst,X27: lst > $o] :
( ( ( X27 @ ( esk4_2 @ X26 @ X27 ) )
| ( X27 @ X26 )
| ~ ( X27 @ nl ) )
& ( ~ ( X27 @ ( cns @ ( esk3_2 @ X26 @ X27 ) @ ( esk4_2 @ X26 @ X27 ) ) )
| ( X27 @ X26 )
| ~ ( X27 @ nl ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_0_lst_Oinduct])])])])]) ).
thf(c_0_6,negated_conjecture,
( ( ap @ xs @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ xs @ esk1_0 ) @ esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
thf(c_0_7,plain,
! [X1: lst,X2: lst > $o] :
( ( X2 @ ( esk4_2 @ X1 @ X2 ) )
| ( X2 @ X1 )
| ~ ( X2 @ nl ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
( ( ap @ xs @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ xs @ esk1_0 ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X25: lst] :
( ( ap @ nl @ X25 )
= X25 ),
inference(variable_rename,[status(thm)],[fact_2p_Osimps_I1_J]) ).
thf(c_0_10,plain,
! [X1: lst,X2: lst > $o] :
( ( X2 @ X1 )
| ~ ( X2 @ ( cns @ ( esk3_2 @ X1 @ X2 ) @ ( esk4_2 @ X1 @ X2 ) ) )
| ~ ( X2 @ nl ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,plain,
! [X22: lst,X23: lst,X24: a] :
( ( ap @ ( cns @ X24 @ X23 ) @ X22 )
= ( cns @ X24 @ ( ap @ X23 @ X22 ) ) ),
inference(variable_rename,[status(thm)],[fact_1p_Osimps_I2_J]) ).
thf(c_0_12,plain,
! [X1: lst] :
( ( ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 ) )
| ( ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap
@ ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ esk1_0 )
@ esk2_0 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_7,c_0_8]) ).
thf(c_0_13,plain,
! [X1: lst] :
( ( ap @ nl @ X1 )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,plain,
! [X1: lst] :
( ( ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 ) )
| ( ( ap @ nl @ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap @ ( ap @ nl @ esk1_0 ) @ esk2_0 ) )
| ( ( ap
@ ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) )
!= ( ap
@ ( ap
@ ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ esk1_0 )
@ esk2_0 ) ) ),
inference(trigger,[status(thm)],[inference(cn,[status(thm)],[]),c_0_10,c_0_8]) ).
thf(c_0_15,plain,
! [X1: lst,X3: a,X4: lst] :
( ( ap @ ( cns @ X3 @ X1 ) @ X4 )
= ( cns @ X3 @ ( ap @ X1 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X1: lst] :
( ( ( ap
@ ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ esk1_0 )
@ esk2_0 )
= ( ap
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) ) )
| ( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13])]) ).
thf(c_0_17,plain,
! [X1: lst] :
( ( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) )
| ( ( ap
@ ( ap
@ ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ esk1_0 )
@ esk2_0 )
!= ( ap
@ ( cns
@ ( esk3_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) )
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13]),c_0_13])]) ).
thf(c_0_18,plain,
! [X3: a,X1: lst] :
( ( ( ap
@ ( ap
@ ( cns @ X3
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ esk1_0 )
@ esk2_0 )
= ( ap
@ ( cns @ X3
@ ( esk4_2 @ X1
@ ^ [Z0: lst] :
( ( ap @ Z0 @ ( ap @ esk1_0 @ esk2_0 ) )
= ( ap @ ( ap @ Z0 @ esk1_0 ) @ esk2_0 ) ) ) )
@ ( ap @ esk1_0 @ esk2_0 ) ) )
| ( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_15]),c_0_15]) ).
thf(c_0_19,plain,
! [X1: lst] :
( ( ap @ ( ap @ X1 @ esk1_0 ) @ esk2_0 )
= ( ap @ X1 @ ( ap @ esk1_0 @ esk2_0 ) ) ),
inference(csr,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT056^2 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n006.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 17:57:54 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.txZLUfnofr/E---3.1_1100775.p
% 0.10/0.25 % Version: 3.5.1-ho
% 0.10/0.25 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting new_ho_14 with 1500s (5) cores
% 0.10/0.25 % Starting full_lambda_8 with 300s (1) cores
% 0.10/0.25 % Starting new_ho_13 with 300s (1) cores
% 0.10/0.25 % Starting ho_unfolding_3 with 300s (1) cores
% 0.10/0.25 % new_ho_14 with pid 1100788 completed with status 0
% 0.10/0.25 % Result found by new_ho_14
% 0.10/0.25 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting new_ho_14 with 1500s (5) cores
% 0.10/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.25 % Search class: HGUSS-FFMF22-DSFFFSBN
% 0.10/0.25 % partial match(3): HGUSS-FFSF21-SSFFFSBN
% 0.10/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.25 % Starting new_ho_14 with 901s (1) cores
% 0.10/0.25 % Starting new_ho_13 with 151s (1) cores
% 0.10/0.25 % Starting new_bool_3 with 151s (1) cores
% 0.10/0.25 % Starting new_bool_1 with 146s (1) cores
% 0.10/0.25 % new_ho_14 with pid 1100793 completed with status 0
% 0.10/0.25 % Result found by new_ho_14
% 0.10/0.25 % Preprocessing class: HSSSSMSSSSSNSFA.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting new_ho_14 with 1500s (5) cores
% 0.10/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.25 % Search class: HGUSS-FFMF22-DSFFFSBN
% 0.10/0.25 % partial match(3): HGUSS-FFSF21-SSFFFSBN
% 0.10/0.25 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.25 % Starting SubtermCWHack with 151s (1) cores
% 0.10/0.25 % Starting new_ho_14 with 901s (1) cores
% 0.10/0.25 % Preprocessing time : 0.002 s
% 0.10/0.25 % Presaturation interreduction done
% 0.10/0.25
% 0.10/0.25 % Proof found!
% 0.10/0.25 % SZS status Theorem
% 0.10/0.25 % SZS output start CNFRefutation
% See solution above
% 0.10/0.25 % Parsed axioms : 10
% 0.10/0.25 % Removed by relevancy pruning/SinE : 6
% 0.10/0.25 % Initial clauses : 5
% 0.10/0.25 % Removed in clause preprocessing : 0
% 0.10/0.25 % Initial clauses in saturation : 13
% 0.10/0.25 % Processed clauses : 36
% 0.10/0.25 % ...of these trivial : 0
% 0.10/0.25 % ...subsumed : 0
% 0.10/0.25 % ...remaining for further processing : 36
% 0.10/0.25 % Other redundant clauses eliminated : 0
% 0.10/0.25 % Clauses deleted for lack of memory : 0
% 0.10/0.25 % Backward-subsumed : 0
% 0.10/0.25 % Backward-rewritten : 3
% 0.10/0.25 % Generated clauses : 28
% 0.10/0.25 % ...of the previous two non-redundant : 17
% 0.10/0.25 % ...aggressively subsumed : 0
% 0.10/0.25 % Contextual simplify-reflections : 1
% 0.10/0.25 % Paramodulations : 26
% 0.10/0.25 % Factorizations : 0
% 0.10/0.25 % NegExts : 0
% 0.10/0.25 % Equation resolutions : 0
% 0.10/0.25 % Disequality decompositions : 0
% 0.10/0.25 % Total rewrite steps : 19
% 0.10/0.25 % ...of those cached : 1
% 0.10/0.25 % Propositional unsat checks : 0
% 0.10/0.25 % Propositional check models : 0
% 0.10/0.25 % Propositional check unsatisfiable : 0
% 0.10/0.25 % Propositional clauses : 0
% 0.10/0.25 % Propositional clauses after purity: 0
% 0.10/0.25 % Propositional unsat core size : 0
% 0.10/0.25 % Propositional preprocessing time : 0.000
% 0.10/0.25 % Propositional encoding time : 0.000
% 0.10/0.25 % Propositional solver time : 0.000
% 0.10/0.25 % Success case prop preproc time : 0.000
% 0.10/0.25 % Success case prop encoding time : 0.000
% 0.10/0.25 % Success case prop solver time : 0.000
% 0.10/0.25 % Current number of processed clauses : 18
% 0.10/0.25 % Positive orientable unit clauses : 12
% 0.10/0.25 % Positive unorientable unit clauses: 0
% 0.10/0.25 % Negative unit clauses : 0
% 0.10/0.25 % Non-unit-clauses : 6
% 0.10/0.25 % Current number of unprocessed clauses: 7
% 0.10/0.25 % ...number of literals in the above : 18
% 0.10/0.25 % Current number of archived formulas : 0
% 0.10/0.25 % Current number of archived clauses : 19
% 0.10/0.25 % Clause-clause subsumption calls (NU) : 36
% 0.10/0.25 % Rec. Clause-clause subsumption calls : 34
% 0.10/0.25 % Non-unit clause-clause subsumptions : 1
% 0.10/0.25 % Unit Clause-clause subsumption calls : 21
% 0.10/0.25 % Rewrite failures with RHS unbound : 0
% 0.10/0.25 % BW rewrite match attempts : 32
% 0.10/0.25 % BW rewrite match successes : 4
% 0.10/0.25 % Condensation attempts : 0
% 0.10/0.25 % Condensation successes : 0
% 0.10/0.25 % Termbank termtop insertions : 4092
% 0.10/0.25 % Search garbage collected termcells : 114
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.007 s
% 0.10/0.25 % System time : 0.004 s
% 0.10/0.25 % Total time : 0.010 s
% 0.10/0.25 % Maximum resident set size: 3640 pages
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.032 s
% 0.10/0.25 % System time : 0.016 s
% 0.10/0.25 % Total time : 0.047 s
% 0.10/0.25 % Maximum resident set size: 4864 pages
% 0.10/0.25 % E exiting
%------------------------------------------------------------------------------