%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV052^5 : 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 08:34:47 AM UTC 2026
% Result : Theorem 0.06s 0.26s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 7 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 196 ( 34 ~; 20 |; 11 &; 128 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 30 ^; 19 !; 3 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
epred1_1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(decl_24,type,
epred2_1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(decl_25,type,
epred3_1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(decl_26,type,
epred4_1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(cTHM120B_pme,conjecture,
? [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X1
@ ^ [X2: $i] : $true
@ ^ [X2: $i] : ~ $true )
& ! [X3: $i > $o] : ( X1 @ X3 @ X3 )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X1 @ X4 @ X5 )
& ( X1 @ X5 @ X6 ) )
=> ( X1 @ X4 @ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IY0MR2D3mJ/E---3.1_838709.p',cTHM120B_pme) ).
thf(c_0_1,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X1
@ ^ [X2: $i] : $true
@ ^ [X2: $i] : ~ $true )
& ! [X3: $i > $o] : ( X1 @ X3 @ X3 )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X1 @ X4 @ X5 )
& ( X1 @ X5 @ X6 ) )
=> ( X1 @ X4 @ X6 ) ) ),
inference(assume_negation,[status(cth)],[cTHM120B_pme]) ).
thf(c_0_2,negated_conjecture,
~ ? [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
& ! [X3: $i > $o] : ( X1 @ X3 @ X3 )
& ! [X4: $i > $o,X5: $i > $o,X6: $i > $o] :
( ( ( X1 @ X4 @ X5 )
& ( X1 @ X5 @ X6 ) )
=> ( X1 @ X4 @ X6 ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X12: ( $i > $o ) > ( $i > $o ) > $o] :
( ( ( X12 @ ( epred2_1 @ X12 ) @ ( epred3_1 @ X12 ) )
| ( X12
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X12 @ ( epred1_1 @ X12 ) @ ( epred1_1 @ X12 ) ) )
& ( ( X12 @ ( epred3_1 @ X12 ) @ ( epred4_1 @ X12 ) )
| ( X12
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X12 @ ( epred1_1 @ X12 ) @ ( epred1_1 @ X12 ) ) )
& ( ~ ( X12 @ ( epred2_1 @ X12 ) @ ( epred4_1 @ X12 ) )
| ( X12
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X12 @ ( epred1_1 @ X12 ) @ ( epred1_1 @ X12 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X1 @ ( epred2_1 @ X1 ) @ ( epred3_1 @ X1 ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X1 @ ( epred1_1 @ X1 ) @ ( epred1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X1 @ ( epred2_1 @ X1 ) @ ( epred4_1 @ X1 ) )
| ~ ( X1 @ ( epred1_1 @ X1 ) @ ( epred1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X1 @ ( epred2_1 @ X1 ) @ ( epred3_1 @ X1 ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X1 @ ( epred1_1 @ X1 ) @ ( epred1_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X1 @ ( epred1_1 @ X1 ) @ ( epred1_1 @ X1 ) )
| ~ ( X1 @ ( epred2_1 @ X1 ) @ ( epred4_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X1 @ ( epred3_1 @ X1 ) @ ( epred4_1 @ X1 ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X1 @ ( epred1_1 @ X1 ) @ ( epred1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
( ( ( epred3_1 @ $eq )
= ( epred2_1 @ $eq ) )
| ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) )
| ( ( epred4_1 @ $eq )
!= ( epred2_1 @ $eq ) ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: ( $i > $o ) > ( $i > $o ) > $o] :
( ( X1 @ ( epred3_1 @ X1 ) @ ( epred4_1 @ X1 ) )
| ( X1
@ ^ [Z0: $i] : $true
@ ^ [Z0: $i] : ~ $true )
| ~ ( X1 @ ( epred1_1 @ X1 ) @ ( epred1_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
( ( epred3_1 @ $eq )
= ( epred2_1 @ $eq ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_9])]) ).
thf(c_0_13,negated_conjecture,
( ( epred4_1 @ $eq )
!= ( epred2_1 @ $eq ) ),
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_10])]) ).
thf(c_0_14,negated_conjecture,
( ( ^ [Z0: $i] : ~ $true )
= ( ^ [Z0: $i] : $true ) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[inference(cn,[status(thm)],[])]),c_0_11]),c_0_12]),c_0_13]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(arg_cong,[status(thm)],[c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV052^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n006.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 15:05:09 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running higher-order theorem proving
% 0.06/0.24 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.IY0MR2D3mJ/E---3.1_838709.p
% 0.06/0.26 % Version: 3.5.1-ho
% 0.06/0.26 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.06/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.26 % Starting post_as_ho5 with 1500s (5) cores
% 0.06/0.26 % Starting sh2lt with 300s (1) cores
% 0.06/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.06/0.26 % Starting post_as_ho10 with 300s (1) cores
% 0.06/0.26 % post_as_ho5 with pid 838722 completed with status 0
% 0.06/0.26 % Result found by post_as_ho5
% 0.06/0.26 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.06/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.26 % Starting post_as_ho5 with 1500s (5) cores
% 0.06/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.06/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.06/0.26 % Search class: HGUNF-FFSF00-SHHFFMBN
% 0.06/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.06/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.06/0.26 % Starting post_as_ho5 with 151s (1) cores
% 0.06/0.26 % Starting ehoh_best_sine with 136s (1) cores
% 0.06/0.26 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 0.06/0.26 % Starting sh2lt with 136s (1) cores
% 0.06/0.26 % SubtermCWHack with pid 838727 completed with status 10
% 0.06/0.26 % Starting sh2l with 136s (1) cores
% 0.06/0.26 % ehoh_best_nonlift_nonlambdatoforall with pid 838731 completed with status 0
% 0.06/0.26 % Result found by ehoh_best_nonlift_nonlambdatoforall
% 0.06/0.26 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.06/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.06/0.26 % Starting post_as_ho5 with 1500s (5) cores
% 0.06/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.06/0.26 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.06/0.26 % Search class: HGUNF-FFSF00-SHHFFMBN
% 0.06/0.26 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.06/0.26 % Starting SubtermCWHack with 136s (1) cores
% 0.06/0.26 % Starting post_as_ho5 with 151s (1) cores
% 0.06/0.26 % Starting ehoh_best_sine with 136s (1) cores
% 0.06/0.26 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 0.06/0.26 % Preprocessing time : 0.001 s
% 0.06/0.26 % Presaturation interreduction done
% 0.06/0.26
% 0.06/0.26 % Proof found!
% 0.06/0.26 % SZS status Theorem
% 0.06/0.26 % SZS output start CNFRefutation
% See solution above
% 0.06/0.26 % Parsed axioms : 1
% 0.06/0.26 % Removed by relevancy pruning/SinE : 0
% 0.06/0.26 % Initial clauses : 3
% 0.06/0.26 % Removed in clause preprocessing : 0
% 0.06/0.26 % Initial clauses in saturation : 3
% 0.06/0.26 % Processed clauses : 25
% 0.06/0.26 % ...of these trivial : 4
% 0.06/0.26 % ...subsumed : 2
% 0.06/0.26 % ...remaining for further processing : 19
% 0.06/0.26 % Other redundant clauses eliminated : 0
% 0.06/0.26 % Clauses deleted for lack of memory : 0
% 0.06/0.26 % Backward-subsumed : 1
% 0.06/0.26 % Backward-rewritten : 4
% 0.06/0.26 % Generated clauses : 57
% 0.06/0.26 % ...of the previous two non-redundant : 39
% 0.06/0.26 % ...aggressively subsumed : 0
% 0.06/0.26 % Contextual simplify-reflections : 0
% 0.06/0.26 % Paramodulations : 2
% 0.06/0.26 % Factorizations : 0
% 0.06/0.26 % NegExts : 2
% 0.06/0.26 % Equation resolutions : 0
% 0.06/0.26 % Disequality decompositions : 0
% 0.06/0.26 % Total rewrite steps : 9
% 0.06/0.26 % ...of those cached : 7
% 0.06/0.26 % Propositional unsat checks : 0
% 0.06/0.26 % Propositional check models : 0
% 0.06/0.26 % Propositional check unsatisfiable : 0
% 0.06/0.26 % Propositional clauses : 0
% 0.06/0.26 % Propositional clauses after purity: 0
% 0.06/0.26 % Propositional unsat core size : 0
% 0.06/0.26 % Propositional preprocessing time : 0.000
% 0.06/0.26 % Propositional encoding time : 0.000
% 0.06/0.26 % Propositional solver time : 0.000
% 0.06/0.26 % Success case prop preproc time : 0.000
% 0.06/0.26 % Success case prop encoding time : 0.000
% 0.30/0.26 % Success case prop solver time : 0.000
% 0.30/0.26 % Current number of processed clauses : 8
% 0.30/0.26 % Positive orientable unit clauses : 2
% 0.30/0.26 % Positive unorientable unit clauses: 0
% 0.30/0.26 % Negative unit clauses : 1
% 0.30/0.26 % Non-unit-clauses : 5
% 0.30/0.26 % Current number of unprocessed clauses: 17
% 0.30/0.26 % ...number of literals in the above : 37
% 0.30/0.26 % Current number of archived formulas : 0
% 0.30/0.26 % Current number of archived clauses : 11
% 0.30/0.26 % Clause-clause subsumption calls (NU) : 4
% 0.30/0.26 % Rec. Clause-clause subsumption calls : 4
% 0.30/0.26 % Non-unit clause-clause subsumptions : 2
% 0.30/0.26 % Unit Clause-clause subsumption calls : 3
% 0.30/0.26 % Rewrite failures with RHS unbound : 0
% 0.30/0.26 % BW rewrite match attempts : 3
% 0.30/0.26 % BW rewrite match successes : 2
% 0.30/0.26 % Condensation attempts : 0
% 0.30/0.26 % Condensation successes : 0
% 0.30/0.26 % Termbank termtop insertions : 3744
% 0.30/0.26 % Search garbage collected termcells : 115
% 0.30/0.26
% 0.30/0.26 % -------------------------------------------------
% 0.30/0.26 % User time : 0.005 s
% 0.30/0.26 % System time : 0.004 s
% 0.30/0.26 % Total time : 0.008 s
% 0.30/0.26 % Maximum resident set size: 3888 pages
% 0.30/0.26
% 0.30/0.26 % -------------------------------------------------
% 0.30/0.26 % User time : 0.020 s
% 0.30/0.26 % System time : 0.014 s
% 0.30/0.26 % Total time : 0.034 s
% 0.30/0.26 % Maximum resident set size: 4608 pages
% 0.30/0.26 % E exiting
%------------------------------------------------------------------------------