%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU557^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:24:30 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 42 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 269 ( 32 ~; 32 |; 18 &; 138 @)
% ( 7 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 18 ^; 58 !; 8 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
exu: ( $i > $o ) > $o ).
thf(decl_24,type,
exuEu: $o ).
thf(decl_25,type,
descr: ( $i > $o ) > $i ).
thf(decl_26,type,
descrp: $o ).
thf(decl_27,type,
esk1_2: ( $i > $o ) > $i > $i ).
thf(decl_28,type,
esk2_2: ( $i > $o ) > $i > $i ).
thf(decl_29,type,
epred1_0: $i > $o ).
thf(decl_30,type,
epred2_0: $i > $o ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(descrp_def,axiom,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( X1
@ ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vbu5Xihm3m/E---3.1_1318591.p',descrp_def) ).
thf(exu_def,axiom,
( exu
= ( ^ [X1: $i > $o] :
? [X2: $i] :
( ( X1 @ X2 )
& ! [X3: $i] :
( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vbu5Xihm3m/E---3.1_1318591.p',exu_def) ).
thf(exuEu_def,axiom,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vbu5Xihm3m/E---3.1_1318591.p',exuEu_def) ).
thf(descr__Cong,conjecture,
( descrp
=> ( exuEu
=> ! [X1: $i > $o,X4: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X4 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X4 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X4 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vbu5Xihm3m/E---3.1_1318591.p',descr__Cong) ).
thf(c_0_4,plain,
( descrp
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[descrp_def]) ).
thf(c_0_5,plain,
( exu
= ( ^ [Z0: $i > $o] :
? [X2: $i] :
( ( Z0 @ X2 )
& ! [X3: $i] :
( ( Z0 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exu_def]) ).
thf(c_0_6,plain,
( exuEu
<=> ! [X1: $i > $o] :
( ( exu
@ ^ [Z0: $i] : ( X1 @ Z0 ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[exuEu_def]) ).
thf(c_0_7,negated_conjecture,
~ ( descrp
=> ( exuEu
=> ! [X1: $i > $o,X4: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X4 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X4 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X4 @ X2 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[descr__Cong]) ).
thf(c_0_8,plain,
( descrp
= ( ! [X1: $i > $o] :
( ? [X15: $i] :
( ( X1 @ X15 )
& ! [X16: $i] :
( ( X1 @ X16 )
=> ( X15 = X16 ) ) )
=> ( X1
@ ( descr
@ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_9,plain,
( exuEu
= ( ! [X1: $i > $o] :
( ? [X13: $i] :
( ( X1 @ X13 )
& ! [X14: $i] :
( ( X1 @ X14 )
=> ( X13 = X14 ) ) )
=> ! [X2: $i,X3: $i] :
( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_5]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X17: $i > $o] :
( ? [X18: $i] :
( ( X17 @ X18 )
& ! [X19: $i] :
( ( X17 @ X19 )
=> ( X18 = X19 ) ) )
=> ( X17
@ ( descr
@ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) )
=> ( ! [X20: $i > $o] :
( ? [X21: $i] :
( ( X20 @ X21 )
& ! [X22: $i] :
( ( X20 @ X22 )
=> ( X21 = X22 ) ) )
=> ! [X23: $i,X24: $i] :
( ( X20 @ X23 )
=> ( ( X20 @ X24 )
=> ( X23 = X24 ) ) ) )
=> ! [X1: $i > $o,X4: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
<=> ( X4 @ X3 ) ) )
=> ( ? [X25: $i] :
( ( X1 @ X25 )
& ! [X26: $i] :
( ( X1 @ X26 )
=> ( X25 = X26 ) ) )
=> ( ? [X27: $i] :
( ( X4 @ X27 )
& ! [X28: $i] :
( ( X4 @ X28 )
=> ( X27 = X28 ) ) )
=> ( ( descr @ X1 )
= ( descr @ X4 ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7]),c_0_8]),c_0_9]),c_0_5])]) ).
thf(c_0_11,negated_conjecture,
! [X29: $i > $o,X30: $i,X32: $i > $o,X33: $i,X35: $i,X36: $i,X39: $i,X40: $i,X42: $i,X44: $i] :
( ( ( X29 @ ( esk1_2 @ X29 @ X30 ) )
| ~ ( X29 @ X30 )
| ( X29 @ ( descr @ X29 ) ) )
& ( ( X30
!= ( esk1_2 @ X29 @ X30 ) )
| ~ ( X29 @ X30 )
| ( X29 @ ( descr @ X29 ) ) )
& ( ( X32 @ ( esk2_2 @ X32 @ X33 ) )
| ~ ( X32 @ X33 )
| ~ ( X32 @ X35 )
| ~ ( X32 @ X36 )
| ( X35 = X36 ) )
& ( ( X33
!= ( esk2_2 @ X32 @ X33 ) )
| ~ ( X32 @ X33 )
| ~ ( X32 @ X35 )
| ~ ( X32 @ X36 )
| ( X35 = X36 ) )
& ( ~ ( epred1_0 @ X39 )
| ( epred2_0 @ X40 )
| ( X39 != X40 ) )
& ( ~ ( epred2_0 @ X40 )
| ( epred1_0 @ X39 )
| ( X39 != X40 ) )
& ( epred1_0 @ esk3_0 )
& ( ~ ( epred1_0 @ X42 )
| ( esk3_0 = X42 ) )
& ( epred2_0 @ esk4_0 )
& ( ~ ( epred2_0 @ X44 )
| ( esk4_0 = X44 ) )
& ( ( descr @ epred1_0 )
!= ( descr @ epred2_0 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X2: $i] :
( ( epred1_0 @ X3 )
| ~ ( epred2_0 @ X2 )
| ( X3 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(er,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
epred2_0 @ esk4_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i] :
( ( esk3_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_16,negated_conjecture,
epred1_0 @ esk4_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X2: $i] :
( ( esk4_0 = X2 )
| ~ ( epred2_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( esk1_2 @ X1 @ X2 ) )
| ( X1 @ ( descr @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_19,negated_conjecture,
esk3_0 = esk4_0,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( descr @ X1 ) )
| ( X2
!= ( esk1_2 @ X1 @ X2 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_21,negated_conjecture,
! [X2: $i] :
( ( ( esk1_2 @ epred2_0 @ X2 )
= esk4_0 )
| ( epred2_0 @ ( descr @ epred2_0 ) )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X2: $i] :
( ( esk4_0 = X2 )
| ~ ( epred1_0 @ X2 ) ),
inference(rw,[status(thm)],[c_0_15,c_0_19]) ).
thf(c_0_23,negated_conjecture,
epred2_0 @ ( descr @ epred2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]),c_0_14])]) ).
thf(c_0_24,negated_conjecture,
! [X2: $i] :
( ( ( esk1_2 @ epred1_0 @ X2 )
= esk4_0 )
| ( epred1_0 @ ( descr @ epred1_0 ) )
| ~ ( epred1_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
thf(c_0_25,negated_conjecture,
( ( descr @ epred1_0 )
!= ( descr @ epred2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_26,negated_conjecture,
( ( descr @ epred2_0 )
= esk4_0 ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
thf(c_0_27,negated_conjecture,
epred1_0 @ ( descr @ epred1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_24])]),c_0_16])]) ).
thf(c_0_28,negated_conjecture,
( ( descr @ epred1_0 )
!= esk4_0 ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU557^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:49:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.vbu5Xihm3m/E---3.1_1318591.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLMCHSA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting pre_casc_6 with 1500s (5) cores
% 0.07/0.25 % Starting new_bool_12 with 300s (1) cores
% 0.07/0.25 % Starting new_bool_6 with 300s (1) cores
% 0.07/0.25 % Starting pre_casc_9 with 300s (1) cores
% 0.07/0.25 % new_bool_12 with pid 1318622 completed with status 0
% 0.07/0.25 % Result found by new_bool_12
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLMCHSA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting pre_casc_6 with 1500s (5) cores
% 0.07/0.25 % Starting new_bool_12 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,1,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1,,1,20000,1.0)
% 0.07/0.25 % Search class: HGUSF-FFSF21-SHSFMSBN
% 0.07/0.25 % partial match(2): HGUSF-FFSF21-SSSFFSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 1318626 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLMCHSA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting pre_casc_6 with 1500s (5) cores
% 0.07/0.25 % Starting new_bool_12 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,1,,1,20000,1.0))
% 0.07/0.25 % SinE strategy is GSinE(CountFormulas,hypos,1,,1,20000,1.0)
% 0.07/0.25 % Search class: HGUSF-FFSF21-SHSFMSBN
% 0.07/0.25 % partial match(2): HGUSF-FFSF21-SSSFFSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 8
% 0.07/0.25 % Removed by relevancy pruning/SinE : 4
% 0.07/0.25 % Initial clauses : 11
% 0.07/0.25 % Removed in clause preprocessing : 0
% 0.07/0.25 % Initial clauses in saturation : 11
% 0.07/0.25 % Processed clauses : 24
% 0.07/0.25 % ...of these trivial : 0
% 0.07/0.25 % ...subsumed : 1
% 0.07/0.25 % ...remaining for further processing : 23
% 0.07/0.25 % Other redundant clauses eliminated : 4
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 8
% 0.07/0.25 % Generated clauses : 21
% 0.07/0.25 % ...of the previous two non-redundant : 16
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 17
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 4
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 16
% 0.07/0.25 % ...of those cached : 10
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 13
% 0.07/0.25 % Positive orientable unit clauses : 5
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 1
% 0.07/0.25 % Non-unit-clauses : 7
% 0.07/0.25 % Current number of unprocessed clauses: 2
% 0.07/0.25 % ...number of literals in the above : 8
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 8
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 11
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 11
% 0.07/0.25 % Non-unit clause-clause subsumptions : 1
% 0.07/0.25 % Unit Clause-clause subsumption calls : 0
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 4
% 0.07/0.25 % BW rewrite match successes : 4
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 1907
% 0.07/0.25 % Search garbage collected termcells : 746
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.002 s
% 0.07/0.25 % System time : 0.004 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3636 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.003 s
% 0.07/0.25 % System time : 0.009 s
% 0.07/0.25 % Total time : 0.012 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------