%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEV242^5 : 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 : 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 08:36:21 AM UTC 2026
% Result : Theorem 0.27s 0.34s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 25 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 119 ( 11 ~; 23 |; 10 &; 60 @)
% ( 5 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 12 ^; 24 !; 7 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
esk1_2: ( $i > $o ) > ( $i > $o ) > $i ).
thf(decl_24,type,
epred1_0: ( $i > $o ) > $o ).
thf(decl_25,type,
epred2_0: $i > $o ).
thf(decl_26,type,
epred3_0: $i > $o ).
thf(decl_27,type,
esk4_0: $i ).
thf(decl_28,type,
epred5_0: $i > $o ).
thf(cTHM4A_pme,conjecture,
( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ! [X4: ( $i > $o ) > $o,X5: $i > $o,X6: $i > $o] :
( ( X4
@ ^ [X7: $i] :
? [X8: $i > $o] :
( ( ( X8 = X5 )
| ( X8 = X6 ) )
& ( X8 @ X7 ) ) )
=> ( X4
@ ^ [X9: $i] :
( ( X5 @ X9 )
| ( X6 @ X9 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nMFs6rIFGa/E---3.1_863138.p',cTHM4A_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ! [X4: ( $i > $o ) > $o,X5: $i > $o,X6: $i > $o] :
( ( X4
@ ^ [X7: $i] :
? [X8: $i > $o] :
( ( ( X8 = X5 )
| ( X8 = X6 ) )
& ( X8 @ X7 ) ) )
=> ( X4
@ ^ [X9: $i] :
( ( X5 @ X9 )
| ( X6 @ X9 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM4A_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ! [X1: $i > $o,X2: $i > $o] :
( ! [X3: $i] :
( ( X1 @ X3 )
<=> ( X2 @ X3 ) )
=> ( X1 = X2 ) )
=> ! [X4: ( $i > $o ) > $o,X5: $i > $o,X6: $i > $o] :
( ( X4
@ ^ [Z0: $i] :
? [X8: $i > $o] :
( ( ( X8 = X5 )
| ( X8 = X6 ) )
& ( X8 @ Z0 ) ) )
=> ( X4
@ ^ [Z0: $i] :
( ( X5 @ Z0 )
| ( X6 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X16: $i > $o,X17: $i > $o] :
( ( ~ ( X16 @ ( esk1_2 @ X16 @ X17 ) )
| ~ ( X17 @ ( esk1_2 @ X16 @ X17 ) )
| ( X16 = X17 ) )
& ( ( X16 @ ( esk1_2 @ X16 @ X17 ) )
| ( X17 @ ( esk1_2 @ X16 @ X17 ) )
| ( X16 = X17 ) )
& ( epred1_0
@ ^ [Z0: $i] :
? [X8: $i > $o] :
( ( ( X8 = epred2_0 )
| ( X8 = epred3_0 ) )
& ( X8 @ Z0 ) ) )
& ~ ( epred1_0
@ ^ [Z0: $i] :
( ( epred2_0 @ Z0 )
| ( epred3_0 @ Z0 ) ) ) ),
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,
~ ( epred1_0
@ ^ [Z0: $i] :
( ( epred2_0 @ Z0 )
| ( epred3_0 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( epred1_0
@ ^ [Z0: $i] :
? [X39: $i > $o] :
( ( ( X39 = epred2_0 )
| ( X39 = epred3_0 ) )
& ( X39 @ Z0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
( ( ^ [Z0: $i] :
? [X40: $i > $o] :
( ( ( X40 = epred2_0 )
| ( X40 = epred3_0 ) )
& ( X40 @ Z0 ) ) )
!= ( ^ [Z0: $i] :
( ( epred2_0 @ Z0 )
| ( epred3_0 @ Z0 ) ) ) ),
inference(ext_sup,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_7,plain,
( ? [X41: $i > $o] :
( ( ( X41 = epred2_0 )
| ( X41 = epred3_0 ) )
& ( X41 @ esk4_0 ) )
<~> ( ( epred2_0 @ esk4_0 )
| ( epred3_0 @ esk4_0 ) ) ),
inference(neg_ext,[status(thm)],[c_0_6]) ).
thf(c_0_8,plain,
~ ( epred2_0 @ esk4_0 ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_7])]) ).
thf(c_0_9,plain,
~ ( epred3_0 @ esk4_0 ),
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_7])]) ).
thf(c_0_10,plain,
( ( epred3_0 = epred5_0 )
| ( epred2_0 = epred5_0 ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_7]),c_0_8]),c_0_9]) ).
thf(c_0_11,plain,
! [X33: $i] :
( ( ( epred3_0 @ X33 )
<=> ( epred5_0 @ X33 ) )
| ( epred2_0 = epred5_0 ) ),
inference(arg_cong,[status(thm)],[c_0_10]) ).
thf(c_0_12,plain,
! [X3: $i] :
( ( epred2_0 = epred5_0 )
| ( epred3_0 @ X3 )
| ~ ( epred5_0 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_13,plain,
epred5_0 @ esk4_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_7]),c_0_8]),c_0_9]) ).
thf(c_0_14,plain,
epred2_0 = epred5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_13])]) ).
thf(c_0_15,plain,
! [X37: $i] :
( ( epred2_0 @ X37 )
<=> ( epred5_0 @ X37 ) ),
inference(arg_cong,[status(thm)],[c_0_14]) ).
thf(c_0_16,plain,
! [X3: $i] :
( ( epred2_0 @ X3 )
| ~ ( epred5_0 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_15]) ).
thf(c_0_17,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV242^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.24 % Computer : n006.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 15:26:39 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 Running higher-order theorem proving
% 0.27/0.30 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.nMFs6rIFGa/E---3.1_863138.p
% 0.27/0.34 % Version: 3.5.1-ho
% 0.27/0.34 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.27/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.34 % Starting post_as_ho5 with 1500s (5) cores
% 0.27/0.34 % Starting sh2lt with 300s (1) cores
% 0.27/0.34 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.27/0.34 % Starting post_as_ho10 with 300s (1) cores
% 0.27/0.34 % post_as_ho5 with pid 863151 completed with status 0
% 0.27/0.34 % Result found by post_as_ho5
% 0.27/0.34 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.27/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.34 % Starting post_as_ho5 with 1500s (5) cores
% 0.27/0.34 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.27/0.34 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.27/0.34 % Search class: HGUSF-FFSF22-DHHFFMBN
% 0.27/0.34 % partial match(1): HGUSF-FFSF22-SHHFFMBN
% 0.27/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.34 % Starting post_as_ho5 with 151s (1) cores
% 0.27/0.34 % Starting sh3 with 271s (1) cores
% 0.27/0.34 % Starting ho_unfolding_3 with 271s (1) cores
% 0.27/0.34 % Starting new_ho_10_cnf2 with 271s (1) cores
% 0.27/0.34 % sh3 with pid 863159 completed with status 0
% 0.27/0.34 % Result found by sh3
% 0.27/0.34 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.27/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.34 % Starting post_as_ho5 with 1500s (5) cores
% 0.27/0.34 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.27/0.34 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.27/0.34 % Search class: HGUSF-FFSF22-DHHFFMBN
% 0.27/0.34 % partial match(1): HGUSF-FFSF22-SHHFFMBN
% 0.27/0.34 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.27/0.34 % Starting SubtermCWHack with 136s (1) cores
% 0.27/0.34 % Starting post_as_ho5 with 151s (1) cores
% 0.27/0.34 % Starting sh3 with 271s (1) cores
% 0.27/0.34 % Preprocessing time : 0.002 s
% 0.27/0.34 % Presaturation interreduction done
% 0.27/0.34
% 0.27/0.34 % Proof found!
% 0.27/0.34 % SZS status Theorem
% 0.27/0.34 % SZS output start CNFRefutation
% See solution above
% 0.27/0.34 % Parsed axioms : 1
% 0.27/0.34 % Removed by relevancy pruning/SinE : 0
% 0.27/0.34 % Initial clauses : 4
% 0.27/0.34 % Removed in clause preprocessing : 0
% 0.27/0.34 % Initial clauses in saturation : 4
% 0.27/0.34 % Processed clauses : 27
% 0.27/0.34 % ...of these trivial : 0
% 0.27/0.34 % ...subsumed : 2
% 0.27/0.34 % ...remaining for further processing : 25
% 0.27/0.34 % Other redundant clauses eliminated : 4
% 0.27/0.34 % Clauses deleted for lack of memory : 0
% 0.27/0.34 % Backward-subsumed : 1
% 0.27/0.34 % Backward-rewritten : 1
% 0.27/0.34 % Generated clauses : 49
% 0.27/0.34 % ...of the previous two non-redundant : 39
% 0.27/0.34 % ...aggressively subsumed : 0
% 0.27/0.34 % Contextual simplify-reflections : 0
% 0.27/0.34 % Paramodulations : 21
% 0.27/0.34 % Factorizations : 2
% 0.27/0.34 % NegExts : 1
% 0.27/0.34 % Equation resolutions : 4
% 0.27/0.34 % Disequality decompositions : 0
% 0.27/0.34 % Total rewrite steps : 14
% 0.27/0.34 % ...of those cached : 12
% 0.27/0.34 % Propositional unsat checks : 0
% 0.27/0.34 % Propositional check models : 0
% 0.27/0.34 % Propositional check unsatisfiable : 0
% 0.27/0.34 % Propositional clauses : 0
% 0.27/0.34 % Propositional clauses after purity: 0
% 0.27/0.34 % Propositional unsat core size : 0
% 0.27/0.34 % Propositional preprocessing time : 0.000
% 0.27/0.34 % Propositional encoding time : 0.000
% 0.27/0.34 % Propositional solver time : 0.000
% 0.27/0.34 % Success case prop preproc time : 0.000
% 0.27/0.34 % Success case prop encoding time : 0.000
% 0.27/0.34 % Success case prop solver time : 0.000
% 0.27/0.34 % Current number of processed clauses : 14
% 0.27/0.34 % Positive orientable unit clauses : 3
% 0.27/0.34 % Positive unorientable unit clauses: 0
% 0.27/0.34 % Negative unit clauses : 4
% 0.27/0.34 % Non-unit-clauses : 7
% 0.27/0.34 % Current number of unprocessed clauses: 15
% 0.27/0.34 % ...number of literals in the above : 60
% 0.27/0.34 % Current number of archived formulas : 0
% 0.27/0.34 % Current number of archived clauses : 11
% 0.27/0.34 % Clause-clause subsumption calls (NU) : 17
% 0.27/0.34 % Rec. Clause-clause subsumption calls : 9
% 0.27/0.34 % Non-unit clause-clause subsumptions : 0
% 0.27/0.34 % Unit Clause-clause subsumption calls : 7
% 0.27/0.34 % Rewrite failures with RHS unbound : 0
% 0.27/0.34 % BW rewrite match attempts : 1
% 0.27/0.34 % BW rewrite match successes : 1
% 0.27/0.34 % Condensation attempts : 0
% 0.27/0.34 % Condensation successes : 0
% 0.27/0.34 % Termbank termtop insertions : 2434
% 0.27/0.34 % Search garbage collected termcells : 210
% 0.27/0.34
% 0.27/0.34 % -------------------------------------------------
% 0.27/0.34 % User time : 0.011 s
% 0.27/0.34 % System time : 0.002 s
% 0.27/0.34 % Total time : 0.013 s
% 0.27/0.34 % Maximum resident set size: 3636 pages
% 0.27/0.34
% 0.27/0.34 % -------------------------------------------------
% 0.27/0.34 % User time : 0.039 s
% 0.27/0.34 % System time : 0.017 s
% 0.27/0.34 % Total time : 0.056 s
% 0.27/0.34 % Maximum resident set size: 4864 pages
% 0.27/0.34 % E exiting
%------------------------------------------------------------------------------