%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU938^5 : 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 : n016.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 08:25:59 AM UTC 2026
% Result : Theorem 0.20s 0.33s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 32 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 304 ( 34 ~; 34 |; 20 &; 195 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 81 ( 33 ^; 48 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
a: $i ).
thf(decl_24,type,
b: $i ).
thf(decl_25,type,
h: $i > $i ).
thf(decl_26,type,
esk1_2: ( $i > $i ) > ( $i > $i ) > $i ).
thf(decl_27,type,
epred1_2: ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ).
thf(decl_28,type,
esk2_3: ( $i > $i ) > ( $i > $i ) > ( ( $i > $i ) > $o ) > $i > $i ).
thf(cTHM196_pme,conjecture,
( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X4: $i > $i,X5: $i > $i] :
( ! [X6: ( $i > $i ) > $o] :
( ( ( X6 @ X4 )
& ! [X7: $i > $i] :
( ( X6 @ X7 )
=> ( X6
@ ^ [X3: $i] : ( X4 @ ( X7 @ X3 ) ) ) ) )
=> ( X6
@ ^ [X3: $i] : ( X5 @ ( X4 @ X3 ) ) ) )
=> ! [X6: ( $i > $i ) > $o] :
( ( ( X6 @ X4 )
& ! [X8: $i > $i] :
( ( X6 @ X8 )
=> ( X6
@ ^ [X3: $i] : ( X4 @ ( X8 @ X3 ) ) ) ) )
=> ( X6 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.62sVw3rEBB/E---3.1_450044.p',cTHM196_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X4: $i > $i,X5: $i > $i] :
( ! [X6: ( $i > $i ) > $o] :
( ( ( X6 @ X4 )
& ! [X7: $i > $i] :
( ( X6 @ X7 )
=> ( X6
@ ^ [X3: $i] : ( X4 @ ( X7 @ X3 ) ) ) ) )
=> ( X6
@ ^ [X3: $i] : ( X5 @ ( X4 @ X3 ) ) ) )
=> ! [X6: ( $i > $i ) > $o] :
( ( ( X6 @ X4 )
& ! [X8: $i > $i] :
( ( X6 @ X8 )
=> ( X6
@ ^ [X3: $i] : ( X4 @ ( X8 @ X3 ) ) ) ) )
=> ( X6 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM196_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) )
=> ( X1 = X2 ) ) )
=> ~ ! [X4: $i > $i,X5: $i > $i] :
( ! [X6: ( $i > $i ) > $o] :
( ( ( X6 @ X4 )
& ! [X7: $i > $i] :
( ( X6 @ X7 )
=> ( X6
@ ^ [Z0: $i] : ( X4 @ ( X7 @ Z0 ) ) ) ) )
=> ( X6
@ ^ [Z0: $i] : ( X5 @ ( X4 @ Z0 ) ) ) )
=> ! [X6: ( $i > $i ) > $o] :
( ( ( X6 @ X4 )
& ! [X8: $i > $i] :
( ( X6 @ X8 )
=> ( X6
@ ^ [Z0: $i] : ( X4 @ ( X8 @ Z0 ) ) ) ) )
=> ( X6 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X18: $i > $i,X19: $i > $i,X21: $i > $i,X22: $i > $i,X24: $i > $i,X25: ( $i > $i ) > $o] :
( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ( ( ( X18 @ ( esk1_2 @ X18 @ X19 ) )
!= ( X19 @ ( esk1_2 @ X18 @ X19 ) ) )
| ( X18 = X19 ) )
& ( ( X25 @ ( esk2_3 @ X21 @ X22 @ X25 ) )
| ~ ( X25 @ X21 )
| ( X25 @ X22 )
| ( epred1_2 @ X21 @ X22 @ X21 ) )
& ( ~ ( X25
@ ^ [Z0: $i] : ( X21 @ ( esk2_3 @ X21 @ X22 @ X25 @ Z0 ) ) )
| ~ ( X25 @ X21 )
| ( X25 @ X22 )
| ( epred1_2 @ X21 @ X22 @ X21 ) )
& ( ( X25 @ ( esk2_3 @ X21 @ X22 @ X25 ) )
| ~ ( X25 @ X21 )
| ( X25 @ X22 )
| ~ ( epred1_2 @ X21 @ X22 @ X24 )
| ( epred1_2 @ X21 @ X22
@ ^ [Z0: $i] : ( X21 @ ( X24 @ Z0 ) ) ) )
& ( ~ ( X25
@ ^ [Z0: $i] : ( X21 @ ( esk2_3 @ X21 @ X22 @ X25 @ Z0 ) ) )
| ~ ( X25 @ X21 )
| ( X25 @ X22 )
| ~ ( epred1_2 @ X21 @ X22 @ X24 )
| ( epred1_2 @ X21 @ X22
@ ^ [Z0: $i] : ( X21 @ ( X24 @ Z0 ) ) ) )
& ( ( X25 @ ( esk2_3 @ X21 @ X22 @ X25 ) )
| ~ ( X25 @ X21 )
| ( X25 @ X22 )
| ~ ( epred1_2 @ X21 @ X22
@ ^ [Z0: $i] : ( X22 @ ( X21 @ Z0 ) ) ) )
& ( ~ ( X25
@ ^ [Z0: $i] : ( X21 @ ( esk2_3 @ X21 @ X22 @ X25 @ Z0 ) ) )
| ~ ( X25 @ X21 )
| ( X25 @ X22 )
| ~ ( epred1_2 @ X21 @ X22
@ ^ [Z0: $i] : ( X22 @ ( X21 @ 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,
! [X1: $i > $i,X2: $i > $i] :
( ( X1 = X2 )
| ( ( X1 @ ( esk1_2 @ X1 @ X2 ) )
!= ( X2 @ ( esk1_2 @ X1 @ X2 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
( ( h @ a )
= a ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X6: ( $i > $i ) > $o,X2: $i > $i,X1: $i > $i] :
( ( X6 @ X2 )
| ( epred1_2 @ X1 @ X2 @ X1 )
| ~ ( X6
@ ^ [Z0: $i] : ( X1 @ ( esk2_3 @ X1 @ X2 @ X6 @ Z0 ) ) )
| ~ ( X6 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i > $i] :
( ( X1
= ( ^ [Z0: $i] : ( h @ a ) ) )
| ( ( X1
@ ( esk1_2 @ X1
@ ^ [Z0: $i] : ( h @ a ) ) )
!= a ) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X6: ( $i > $i ) > $o,X2: $i > $i,X1: $i > $i] :
( ( X6 @ X2 )
| ~ ( X6
@ ^ [Z0: $i] : ( X1 @ ( esk2_3 @ X1 @ X2 @ X6 @ Z0 ) ) )
| ~ ( X6 @ X1 )
| ~ ( epred1_2 @ X1 @ X2
@ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i > $i,X2: $i > $i] :
( ( X1 = X2 )
| ( epred1_2 @ X2 @ X1 @ X2 )
| ( ( ^ [Z0: $i] :
( X2
@ ( esk2_3 @ X2 @ X1
@ ^ [Z1: $i > $i] : ( Z1 = X2 )
@ Z0 ) ) )
!= X2 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_6]) ).
thf(c_0_10,negated_conjecture,
( ( ^ [Z0: $i] : ( h @ a ) )
= ( ^ [Z0: $i] : a ) ),
inference(er,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X2: $i > $i,X1: $i > $i] :
( ( ( ^ [Z0: $i] :
( X1
@ ( esk2_3 @ X1 @ X2
@ ^ [Z1: $i > $i] : ( Z1 != X2 )
@ Z0 ) ) )
= X2 )
| ( X1 = X2 )
| ~ ( epred1_2 @ X1 @ X2
@ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i > $i] :
( ( X1
= ( ^ [Z0: $i] : a ) )
| ( epred1_2
@ ^ [Z0: $i] : a
@ X1
@ ^ [Z0: $i] : a ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_10]),c_0_10]),c_0_10])]) ).
thf(c_0_13,negated_conjecture,
( ( ^ [Z0: $i] : Z0 )
= ( ^ [Z0: $i] : a ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
( ( h @ b )
!= a ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i] : ( X3 = a ),
inference(arg_cong,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU938^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n016.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:52:04 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.62sVw3rEBB/E---3.1_450044.p
% 0.20/0.33 % Version: 3.5.1-ho
% 0.20/0.33 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.20/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.33 % Starting post_as_ho5 with 1500s (5) cores
% 0.20/0.33 % Starting sh2lt with 300s (1) cores
% 0.20/0.33 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.20/0.33 % Starting post_as_ho10 with 300s (1) cores
% 0.20/0.33 % post_as_ho5 with pid 450072 completed with status 0
% 0.20/0.33 % Result found by post_as_ho5
% 0.20/0.33 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.20/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.33 % Starting post_as_ho5 with 1500s (5) cores
% 0.20/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.20/0.33 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.20/0.33 % Search class: HGUSF-FFSF32-MHHFFMBN
% 0.20/0.33 % partial match(2): HGUNF-FFSF32-SHHFFMBN
% 0.20/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.33 % Starting post_as_ho5 with 151s (1) cores
% 0.20/0.33 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.20/0.33 % Starting sh5l with 136s (1) cores
% 0.20/0.33 % Starting new_bool_3 with 136s (1) cores
% 0.20/0.33 % SubtermCWHack with pid 450078 completed with status 10
% 0.20/0.33 % Starting new_bool_2 with 136s (1) cores
% 0.20/0.33 % post_as_ho5 with pid 450079 completed with status 0
% 0.20/0.33 % Result found by post_as_ho5
% 0.20/0.33 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.20/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.33 % Starting post_as_ho5 with 1500s (5) cores
% 0.20/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.20/0.33 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.20/0.33 % Search class: HGUSF-FFSF32-MHHFFMBN
% 0.20/0.33 % partial match(2): HGUNF-FFSF32-SHHFFMBN
% 0.20/0.33 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.33 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.33 % Starting post_as_ho5 with 151s (1) cores
% 0.20/0.33 % Preprocessing time : 0.001 s
% 0.20/0.33 % Presaturation interreduction done
% 0.20/0.33
% 0.20/0.33 % Proof found!
% 0.20/0.33 % SZS status Theorem
% 0.20/0.33 % SZS output start CNFRefutation
% See solution above
% 0.20/0.33 % Parsed axioms : 4
% 0.20/0.33 % Removed by relevancy pruning/SinE : 3
% 0.20/0.33 % Initial clauses : 9
% 0.20/0.33 % Removed in clause preprocessing : 0
% 0.20/0.33 % Initial clauses in saturation : 9
% 0.20/0.33 % Processed clauses : 58
% 0.20/0.33 % ...of these trivial : 0
% 0.20/0.33 % ...subsumed : 15
% 0.20/0.33 % ...remaining for further processing : 43
% 0.20/0.33 % Other redundant clauses eliminated : 14
% 0.20/0.33 % Clauses deleted for lack of memory : 0
% 0.20/0.33 % Backward-subsumed : 2
% 0.20/0.33 % Backward-rewritten : 15
% 0.20/0.33 % Generated clauses : 355
% 0.20/0.33 % ...of the previous two non-redundant : 307
% 0.20/0.33 % ...aggressively subsumed : 0
% 0.20/0.33 % Contextual simplify-reflections : 0
% 0.20/0.33 % Paramodulations : 279
% 0.20/0.33 % Factorizations : 2
% 0.20/0.33 % NegExts : 2
% 0.20/0.33 % Equation resolutions : 33
% 0.20/0.33 % Disequality decompositions : 0
% 0.20/0.33 % Total rewrite steps : 61
% 0.20/0.33 % ...of those cached : 52
% 0.20/0.33 % Propositional unsat checks : 0
% 0.20/0.33 % Propositional check models : 0
% 0.20/0.33 % Propositional check unsatisfiable : 0
% 0.20/0.33 % Propositional clauses : 0
% 0.20/0.33 % Propositional clauses after purity: 0
% 0.20/0.33 % Propositional unsat core size : 0
% 0.20/0.33 % Propositional preprocessing time : 0.000
% 0.20/0.33 % Propositional encoding time : 0.000
% 0.20/0.33 % Propositional solver time : 0.000
% 0.20/0.33 % Success case prop preproc time : 0.000
% 0.20/0.33 % Success case prop encoding time : 0.000
% 0.20/0.33 % Success case prop solver time : 0.000
% 0.20/0.33 % Current number of processed clauses : 17
% 0.20/0.33 % Positive orientable unit clauses : 1
% 0.20/0.33 % Positive unorientable unit clauses: 1
% 0.20/0.33 % Negative unit clauses : 0
% 0.20/0.33 % Non-unit-clauses : 15
% 0.20/0.33 % Current number of unprocessed clauses: 267
% 0.20/0.33 % ...number of literals in the above : 1009
% 0.20/0.33 % Current number of archived formulas : 0
% 0.20/0.33 % Current number of archived clauses : 26
% 0.20/0.33 % Clause-clause subsumption calls (NU) : 84
% 0.20/0.33 % Rec. Clause-clause subsumption calls : 46
% 0.20/0.33 % Non-unit clause-clause subsumptions : 15
% 0.20/0.33 % Unit Clause-clause subsumption calls : 9
% 0.20/0.33 % Rewrite failures with RHS unbound : 0
% 0.20/0.33 % BW rewrite match attempts : 50
% 0.20/0.33 % BW rewrite match successes : 17
% 0.20/0.33 % Condensation attempts : 0
% 0.20/0.33 % Condensation successes : 0
% 0.20/0.33 % Termbank termtop insertions : 37356
% 0.20/0.33 % Search garbage collected termcells : 376
% 0.20/0.33
% 0.20/0.33 % -------------------------------------------------
% 0.20/0.33 % User time : 0.037 s
% 0.20/0.33 % System time : 0.006 s
% 0.20/0.33 % Total time : 0.043 s
% 0.20/0.33 % Maximum resident set size: 3640 pages
% 0.20/0.33
% 0.20/0.33 % -------------------------------------------------
% 0.20/0.33 % User time : 0.337 s
% 0.20/0.33 % System time : 0.023 s
% 0.20/0.33 % Total time : 0.359 s
% 0.20/0.33 % Maximum resident set size: 4864 pages
% 0.20/0.33 % E exiting
%------------------------------------------------------------------------------