%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV018^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:34:44 AM UTC 2026
% Result : Theorem 0.09s 0.16s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 10 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 357 ( 46 ~; 44 |; 24 &; 225 @)
% ( 5 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 2 ^; 55 !; 12 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
epred1_0: ( a > $o ) > $o ).
thf(decl_24,type,
esk1_1: ( a > $o ) > a ).
thf(decl_25,type,
epred2_1: a > a > $o ).
thf(decl_26,type,
epred3_1: ( a > a > $o ) > a > $o ).
thf(decl_27,type,
esk2_1: ( a > a > $o ) > a ).
thf(decl_28,type,
esk3_1: ( a > a > $o ) > a ).
thf(decl_29,type,
esk4_1: ( a > a > $o ) > a ).
thf(decl_30,type,
esk4_2: a > ( a > a > $o ) > a ).
thf(cTHM262A_pme,conjecture,
! [X1: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ? [X3: a] : ( X2 @ X3 ) )
& ! [X4: a] :
? [X2: a > $o] :
( ( X1 @ X2 )
& ( X2 @ X4 )
& ! [X5: a > $o] :
( ( ( X1 @ X5 )
& ( X5 @ X4 ) )
=> ( X5 = X2 ) ) ) )
=> ? [X6: a > a > $o] :
( ( ^ [X7: a > $o] :
( ? [X3: a] : ( X7 @ X3 )
& ! [X4: a] :
( ( X7 @ X4 )
=> ! [X8: a] :
( ( X7 @ X8 )
<=> ( X6 @ X4 @ X8 ) ) ) ) )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.4CI2fhbBzA/E---3.1_220176.p',cTHM262A_pme) ).
thf(c_0_1,negated_conjecture,
~ ! [X1: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ? [X3: a] : ( X2 @ X3 ) )
& ! [X4: a] :
? [X2: a > $o] :
( ( X1 @ X2 )
& ( X2 @ X4 )
& ! [X5: a > $o] :
( ( ( X1 @ X5 )
& ( X5 @ X4 ) )
=> ( X5 = X2 ) ) ) )
=> ? [X6: a > a > $o] :
( ( ^ [X7: a > $o] :
( ? [X3: a] : ( X7 @ X3 )
& ! [X4: a] :
( ( X7 @ X4 )
=> ! [X8: a] :
( ( X7 @ X8 )
<=> ( X6 @ X4 @ X8 ) ) ) ) )
= X1 ) ),
inference(assume_negation,[status(cth)],[cTHM262A_pme]) ).
thf(c_0_2,negated_conjecture,
~ ! [X1: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X1 @ X2 )
=> ? [X3: a] : ( X2 @ X3 ) )
& ! [X4: a] :
? [X2: a > $o] :
( ( X1 @ X2 )
& ( X2 @ X4 )
& ! [X5: a > $o] :
( ( ( X1 @ X5 )
& ( X5 @ X4 ) )
=> ( X5 = X2 ) ) ) )
=> ? [X6: a > a > $o] :
! [X16: a > $o] :
( ( ? [X3: a] : ( X16 @ X3 )
& ! [X4: a] :
( ( X16 @ X4 )
=> ! [X8: a] :
( ( X16 @ X8 )
<=> ( X6 @ X4 @ X8 ) ) ) )
<=> ( X1 @ X16 ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X18: a > $o,X20: a,X22: a > $o,X23: a > a > $o,X25: a,X29: a,X30: a] :
( ( ~ ( epred1_0 @ X18 )
| ( X18 @ ( esk1_1 @ X18 ) ) )
& ( epred1_0 @ ( epred2_1 @ X20 ) )
& ( epred2_1 @ X20 @ X20 )
& ( ~ ( epred1_0 @ X22 )
| ~ ( X22 @ X20 )
| ( X22
= ( epred2_1 @ X20 ) ) )
& ( ( epred3_1 @ X23 @ ( esk2_1 @ X23 ) )
| ~ ( epred3_1 @ X23 @ X25 )
| ~ ( epred1_0 @ ( epred3_1 @ X23 ) ) )
& ( ~ ( epred3_1 @ X23 @ ( esk3_1 @ X23 ) )
| ~ ( X23 @ ( esk2_1 @ X23 ) @ ( esk3_1 @ X23 ) )
| ~ ( epred3_1 @ X23 @ X25 )
| ~ ( epred1_0 @ ( epred3_1 @ X23 ) ) )
& ( ( epred3_1 @ X23 @ ( esk3_1 @ X23 ) )
| ( X23 @ ( esk2_1 @ X23 ) @ ( esk3_1 @ X23 ) )
| ~ ( epred3_1 @ X23 @ X25 )
| ~ ( epred1_0 @ ( epred3_1 @ X23 ) ) )
& ( ( epred3_1 @ X23 @ ( esk4_1 @ X23 ) )
| ( epred1_0 @ ( epred3_1 @ X23 ) ) )
& ( ~ ( epred3_1 @ X23 @ X30 )
| ( X23 @ X29 @ X30 )
| ~ ( epred3_1 @ X23 @ X29 )
| ( epred1_0 @ ( epred3_1 @ X23 ) ) )
& ( ~ ( X23 @ X29 @ X30 )
| ( epred3_1 @ X23 @ X30 )
| ~ ( epred3_1 @ X23 @ X29 )
| ( epred1_0 @ ( epred3_1 @ X23 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X3: a,X6: a > a > $o,X4: a] :
( ( X6 @ X4 @ X3 )
| ( epred1_0 @ ( epred3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ X3 )
| ~ ( epred3_1 @ X6 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X3: a] :
( ( epred1_0 @ ( epred3_1 @ $neq ) )
| ~ ( epred3_1 @ $neq @ X3 ) ),
inference(er,[status(thm)],[inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_4])]) ).
thf(c_0_6,negated_conjecture,
! [X6: a > a > $o] :
( ( epred3_1 @ X6 @ ( esk4_1 @ X6 ) )
| ( epred1_0 @ ( epred3_1 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X3: a,X6: a > a > $o] :
( ( epred3_1 @ X6 @ ( esk2_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ X3 )
| ~ ( epred1_0 @ ( epred3_1 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
epred1_0 @ ( epred3_1 @ $neq ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X2: a > $o] :
( ( X2 @ ( esk1_1 @ X2 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_10,negated_conjecture,
! [X2: a > $o,X3: a] :
( ( X2
= ( epred2_1 @ X3 ) )
| ~ ( epred1_0 @ X2 )
| ~ ( X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_11,negated_conjecture,
! [X3: a] :
( ( epred3_1 @ $neq @ ( esk2_1 @ $neq ) )
| ~ ( epred3_1 @ $neq @ X3 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,negated_conjecture,
epred3_1 @ $neq @ ( esk1_1 @ ( epred3_1 @ $neq ) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
thf(c_0_13,negated_conjecture,
! [X3: a,X6: a > a > $o] :
( ~ ( epred3_1 @ X6 @ ( esk3_1 @ X6 ) )
| ~ ( X6 @ ( esk2_1 @ X6 ) @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ X3 )
| ~ ( epred1_0 @ ( epred3_1 @ X6 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_14,negated_conjecture,
! [X3: a] : ( epred1_0 @ ( epred2_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,negated_conjecture,
! [X3: a] :
( ( ( epred3_1 @ $neq )
= ( epred2_1 @ X3 ) )
| ~ ( epred3_1 @ $neq @ X3 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
thf(c_0_16,negated_conjecture,
epred3_1 @ $neq @ ( esk2_1 @ $neq ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_17,plain,
! [X3: a,X6: a > a > $o,X4: a] :
( ( ( epred3_1 @ X6 )
!= ( epred2_1 @ X3 ) )
| ~ ( X6 @ ( esk2_1 @ X6 ) @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ X4 ) ),
inference(ext_sup,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( epred2_1 @ ( esk2_1 @ $neq ) )
= ( epred3_1 @ $neq ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,plain,
! [X3: a,X6: a > a > $o,X4: a] :
( ( ( epred3_1 @ X6 @ ( esk4_2 @ X3 @ X6 ) )
<~> ( epred2_1 @ X3 @ ( esk4_2 @ X3 @ X6 ) ) )
| ~ ( X6 @ ( esk2_1 @ X6 ) @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ X4 ) ),
inference(neg_ext,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X42: a] :
( ( epred2_1 @ ( esk2_1 @ $neq ) @ X42 )
<=> ( epred3_1 @ $neq @ X42 ) ),
inference(arg_cong,[status(thm)],[c_0_18]) ).
thf(c_0_21,plain,
! [X3: a,X6: a > a > $o,X4: a] :
( ~ ( epred3_1 @ X6 @ ( esk4_2 @ X3 @ X6 ) )
| ~ ( epred2_1 @ X3 @ ( esk4_2 @ X3 @ X6 ) )
| ~ ( X6 @ ( esk2_1 @ X6 ) @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ ( esk3_1 @ X6 ) )
| ~ ( epred3_1 @ X6 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
! [X3: a] : ( epred3_1 @ $true @ X3 ),
inference(dynamic_cnf,[status(thm)],[c_0_20]) ).
thf(c_0_23,plain,
! [X3: a] :
( ~ ( $true @ ( esk2_1 @ $true ) @ ( esk3_1 @ $true ) )
| ~ ( epred2_1 @ X3 @ ( esk4_2 @ X3 @ $true ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]),c_0_22])]) ).
thf(c_0_24,plain,
! [X3: a] :
~ ( epred2_1 @ X3 @ ( esk4_2 @ X3 @ $true ) ),
inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_23])]) ).
thf(c_0_25,negated_conjecture,
! [X3: a] : ( epred2_1 @ ( esk2_1 @ $true ) @ X3 ),
inference(dynamic_cnf,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
$false,
inference(spm,[status(thm)],[c_0_24,c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV018^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 15:00:18 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.13 Running higher-order theorem proving
% 0.09/0.14 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.4CI2fhbBzA/E---3.1_220176.p
% 0.09/0.16 % Version: 3.5.1-ho
% 0.09/0.16 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.09/0.16 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting sh2lt with 1200s (4) cores
% 0.09/0.16 % Starting new_ho_10_unif with 300s (1) cores
% 0.09/0.16 % Starting full_lambda_6 with 300s (1) cores
% 0.09/0.16 % Starting post_as_ho1 with 300s (1) cores
% 0.09/0.16 % Starting ehoh_best3_rw with 300s (1) cores
% 0.09/0.16 % sh2lt with pid 220189 completed with status 0
% 0.09/0.16 % Result found by sh2lt
% 0.09/0.16 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.09/0.16 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting sh2lt with 1200s (4) cores
% 0.09/0.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.09/0.16 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.09/0.16 % Search class: HGHSS-FFSF11-SHHFFMBN
% 0.09/0.16 % partial match(1): HGHSS-FFMF11-SHHFFMBN
% 0.09/0.16 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.09/0.16 % Starting SubtermCWHack with 109s (1) cores
% 0.09/0.16 % Starting sh2lt with 121s (1) cores
% 0.09/0.16 % Starting ho_unfolding_1 with 109s (1) cores
% 0.09/0.16 % Starting ho_unfolding_4 with 109s (1) cores
% 0.09/0.16 % sh2lt with pid 220196 completed with status 0
% 0.09/0.16 % Result found by sh2lt
% 0.09/0.16 % Preprocessing class: HSSSSMSSSSSNHHA.
% 0.09/0.16 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.16 % Starting sh2lt with 1200s (4) cores
% 0.09/0.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,5,,4,20000,1.0,true))
% 0.09/0.16 % SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 0.09/0.16 % Search class: HGHSS-FFSF11-SHHFFMBN
% 0.09/0.16 % partial match(1): HGHSS-FFMF11-SHHFFMBN
% 0.09/0.16 % Scheduled 7 strats onto 4 cores with 1200 seconds (1200 total)
% 0.09/0.16 % Starting SubtermCWHack with 109s (1) cores
% 0.09/0.16 % Starting sh2lt with 121s (1) cores
% 0.09/0.16 % Preprocessing time : 0.001 s
% 0.09/0.16 % Presaturation interreduction done
% 0.09/0.16
% 0.09/0.16 % Proof found!
% 0.09/0.16 % SZS status Theorem
% 0.09/0.16 % SZS output start CNFRefutation
% See solution above
% 0.09/0.16 % Parsed axioms : 2
% 0.09/0.16 % Removed by relevancy pruning/SinE : 1
% 0.09/0.16 % Initial clauses : 10
% 0.09/0.16 % Removed in clause preprocessing : 0
% 0.09/0.16 % Initial clauses in saturation : 10
% 0.09/0.16 % Processed clauses : 57
% 0.09/0.16 % ...of these trivial : 1
% 0.09/0.16 % ...subsumed : 2
% 0.09/0.16 % ...remaining for further processing : 54
% 0.09/0.16 % Other redundant clauses eliminated : 4
% 0.09/0.16 % Clauses deleted for lack of memory : 0
% 0.09/0.16 % Backward-subsumed : 0
% 0.09/0.16 % Backward-rewritten : 3
% 0.09/0.16 % Generated clauses : 115
% 0.09/0.16 % ...of the previous two non-redundant : 74
% 0.09/0.16 % ...aggressively subsumed : 0
% 0.09/0.16 % Contextual simplify-reflections : 0
% 0.09/0.16 % Paramodulations : 44
% 0.09/0.16 % Factorizations : 0
% 0.09/0.16 % NegExts : 1
% 0.09/0.16 % Equation resolutions : 4
% 0.09/0.16 % Disequality decompositions : 0
% 0.09/0.16 % Total rewrite steps : 34
% 0.09/0.16 % ...of those cached : 18
% 0.09/0.16 % Propositional unsat checks : 0
% 0.09/0.16 % Propositional check models : 0
% 0.09/0.16 % Propositional check unsatisfiable : 0
% 0.09/0.16 % Propositional clauses : 0
% 0.09/0.16 % Propositional clauses after purity: 0
% 0.09/0.16 % Propositional unsat core size : 0
% 0.09/0.16 % Propositional preprocessing time : 0.000
% 0.09/0.16 % Propositional encoding time : 0.000
% 0.09/0.16 % Propositional solver time : 0.000
% 0.09/0.16 % Success case prop preproc time : 0.000
% 0.09/0.16 % Success case prop encoding time : 0.000
% 0.09/0.16 % Success case prop solver time : 0.000
% 0.09/0.16 % Current number of processed clauses : 35
% 0.09/0.16 % Positive orientable unit clauses : 13
% 0.09/0.16 % Positive unorientable unit clauses: 0
% 0.09/0.16 % Negative unit clauses : 2
% 0.09/0.16 % Non-unit-clauses : 20
% 0.09/0.16 % Current number of unprocessed clauses: 37
% 0.09/0.16 % ...number of literals in the above : 105
% 0.09/0.16 % Current number of archived formulas : 0
% 0.09/0.16 % Current number of archived clauses : 19
% 0.09/0.16 % Clause-clause subsumption calls (NU) : 40
% 0.09/0.16 % Rec. Clause-clause subsumption calls : 14
% 0.09/0.16 % Non-unit clause-clause subsumptions : 2
% 0.09/0.16 % Unit Clause-clause subsumption calls : 25
% 0.09/0.16 % Rewrite failures with RHS unbound : 0
% 0.09/0.16 % BW rewrite match attempts : 3
% 0.09/0.16 % BW rewrite match successes : 2
% 0.09/0.16 % Condensation attempts : 0
% 0.09/0.16 % Condensation successes : 0
% 0.09/0.16 % Termbank termtop insertions : 4843
% 0.09/0.16 % Search garbage collected termcells : 477
% 0.09/0.16
% 0.09/0.16 % -------------------------------------------------
% 0.09/0.16 % User time : 0.005 s
% 0.09/0.16 % System time : 0.002 s
% 0.09/0.16 % Total time : 0.007 s
% 0.09/0.16 % Maximum resident set size: 3640 pages
% 0.09/0.16
% 0.09/0.16 % -------------------------------------------------
% 0.09/0.16 % User time : 0.023 s
% 0.09/0.16 % System time : 0.006 s
% 0.09/0.16 % Total time : 0.029 s
% 0.09/0.16 % Maximum resident set size: 4864 pages
% 0.09/0.16 % E exiting
%------------------------------------------------------------------------------