%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU972^5 : 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 : n020.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 08:28:11 AM UTC 2026
% Result : Theorem 0.12s 0.28s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 68 ( 67 equ; 0 cnn)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 433 ( 31 ~; 27 |; 41 &; 310 @)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 66 ( 8 ^; 55 !; 3 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
cR: a > a ).
thf(decl_24,type,
cP: a > a > a ).
thf(decl_25,type,
cL: a > a ).
thf(decl_26,type,
cZ: a ).
thf(decl_27,type,
esk1_1: ( a > $o ) > a ).
thf(decl_28,type,
esk2_1: ( a > $o ) > a ).
thf(decl_29,type,
esk3_0: a ).
thf(decl_30,type,
esk4_1: ( a > $o ) > a ).
thf(decl_31,type,
esk5_1: ( a > $o ) > a ).
thf(cPU_LEM2E_pme,conjecture,
( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a] :
( ( X3 != cZ )
<=> ( X3
= ( cP @ ( cL @ X3 ) @ ( cR @ X3 ) ) ) )
& ! [X4: a > $o] :
( ! [X3: a,X5: a] :
( ( X4 @ ( cP @ X3 @ X5 ) )
=> ( ( ( X3 = cZ )
<=> ( X5 = cZ ) )
& ( X4 @ ( cP @ ( cL @ X3 ) @ ( cL @ X5 ) ) )
& ( X4 @ ( cP @ ( cR @ X3 ) @ ( cR @ X5 ) ) ) ) )
=> ! [X3: a,X5: a] :
( ( X4 @ ( cP @ X3 @ X5 ) )
=> ( X3 = X5 ) ) ) )
=> ! [X3: a] :
? [X4: a > $o] :
( ( X4 @ ( cP @ cZ @ X3 ) )
& ! [X6: a,X5: a] :
( ( X4 @ ( cP @ X6 @ X5 ) )
=> ( ( ( X5 = cZ )
=> ( X6 = cZ ) )
& ( X4 @ ( cP @ ( cL @ X6 ) @ ( cL @ X5 ) ) )
& ( X4 @ ( cP @ ( cR @ X6 ) @ ( cR @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PvzQxa6QTn/E---3.1_1153905.p',cPU_LEM2E_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a] :
( ( X3 != cZ )
<=> ( X3
= ( cP @ ( cL @ X3 ) @ ( cR @ X3 ) ) ) )
& ! [X4: a > $o] :
( ! [X3: a,X5: a] :
( ( X4 @ ( cP @ X3 @ X5 ) )
=> ( ( ( X3 = cZ )
<=> ( X5 = cZ ) )
& ( X4 @ ( cP @ ( cL @ X3 ) @ ( cL @ X5 ) ) )
& ( X4 @ ( cP @ ( cR @ X3 ) @ ( cR @ X5 ) ) ) ) )
=> ! [X3: a,X5: a] :
( ( X4 @ ( cP @ X3 @ X5 ) )
=> ( X3 = X5 ) ) ) )
=> ! [X3: a] :
? [X4: a > $o] :
( ( X4 @ ( cP @ cZ @ X3 ) )
& ! [X6: a,X5: a] :
( ( X4 @ ( cP @ X6 @ X5 ) )
=> ( ( ( X5 = cZ )
=> ( X6 = cZ ) )
& ( X4 @ ( cP @ ( cL @ X6 ) @ ( cL @ X5 ) ) )
& ( X4 @ ( cP @ ( cR @ X6 ) @ ( cR @ X5 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPU_LEM2E_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ! [X1: a,X2: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a] :
( ( X3 != cZ )
<=> ( X3
= ( cP @ ( cL @ X3 ) @ ( cR @ X3 ) ) ) )
& ! [X4: a > $o] :
( ! [X3: a,X5: a] :
( ( X4 @ ( cP @ X3 @ X5 ) )
=> ( ( ( X3 = cZ )
<=> ( X5 = cZ ) )
& ( X4 @ ( cP @ ( cL @ X3 ) @ ( cL @ X5 ) ) )
& ( X4 @ ( cP @ ( cR @ X3 ) @ ( cR @ X5 ) ) ) ) )
=> ! [X3: a,X5: a] :
( ( X4 @ ( cP @ X3 @ X5 ) )
=> ( X3 = X5 ) ) ) )
=> ! [X3: a] :
? [X4: a > $o] :
( ( X4 @ ( cP @ cZ @ X3 ) )
& ! [X6: a,X5: a] :
( ( X4 @ ( cP @ X6 @ X5 ) )
=> ( ( ( X5 = cZ )
=> ( X6 = cZ ) )
& ( X4 @ ( cP @ ( cL @ X6 ) @ ( cL @ X5 ) ) )
& ( X4 @ ( cP @ ( cR @ X6 ) @ ( cR @ X5 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X21: a,X22: a,X23: a,X24: a,X25: a,X26: a > $o,X29: a,X30: a,X32: a > $o] :
( ( ( cL @ cZ )
= cZ )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ ( cP @ X21 @ X22 ) )
= X21 )
& ( ( cR @ ( cP @ X23 @ X24 ) )
= X24 )
& ( ( X25 = cZ )
| ( X25
= ( cP @ ( cL @ X25 ) @ ( cR @ X25 ) ) ) )
& ( ( X25
!= ( cP @ ( cL @ X25 ) @ ( cR @ X25 ) ) )
| ( X25 != cZ ) )
& ( ( X26 @ ( cP @ ( esk1_1 @ X26 ) @ ( esk2_1 @ X26 ) ) )
| ~ ( X26 @ ( cP @ X29 @ X30 ) )
| ( X29 = X30 ) )
& ( ( ( esk1_1 @ X26 )
!= cZ )
| ( ( esk2_1 @ X26 )
!= cZ )
| ~ ( X26 @ ( cP @ ( cL @ ( esk1_1 @ X26 ) ) @ ( cL @ ( esk2_1 @ X26 ) ) ) )
| ~ ( X26 @ ( cP @ ( cR @ ( esk1_1 @ X26 ) ) @ ( cR @ ( esk2_1 @ X26 ) ) ) )
| ~ ( X26 @ ( cP @ X29 @ X30 ) )
| ( X29 = X30 ) )
& ( ( ( esk1_1 @ X26 )
= cZ )
| ( ( esk2_1 @ X26 )
= cZ )
| ~ ( X26 @ ( cP @ ( cL @ ( esk1_1 @ X26 ) ) @ ( cL @ ( esk2_1 @ X26 ) ) ) )
| ~ ( X26 @ ( cP @ ( cR @ ( esk1_1 @ X26 ) ) @ ( cR @ ( esk2_1 @ X26 ) ) ) )
| ~ ( X26 @ ( cP @ X29 @ X30 ) )
| ( X29 = X30 ) )
& ( ( X32 @ ( cP @ ( esk4_1 @ X32 ) @ ( esk5_1 @ X32 ) ) )
| ~ ( X32 @ ( cP @ cZ @ esk3_0 ) ) )
& ( ( ( esk5_1 @ X32 )
= cZ )
| ~ ( X32 @ ( cP @ ( cL @ ( esk4_1 @ X32 ) ) @ ( cL @ ( esk5_1 @ X32 ) ) ) )
| ~ ( X32 @ ( cP @ ( cR @ ( esk4_1 @ X32 ) ) @ ( cR @ ( esk5_1 @ X32 ) ) ) )
| ~ ( X32 @ ( cP @ cZ @ esk3_0 ) ) )
& ( ( ( esk4_1 @ X32 )
!= cZ )
| ~ ( X32 @ ( cP @ ( cL @ ( esk4_1 @ X32 ) ) @ ( cL @ ( esk5_1 @ X32 ) ) ) )
| ~ ( X32 @ ( cP @ ( cR @ ( esk4_1 @ X32 ) ) @ ( cR @ ( esk5_1 @ X32 ) ) ) )
| ~ ( X32 @ ( cP @ cZ @ esk3_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(fof_nnf,[status(thm)],[c_0_2])])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X4: a > $o] :
( ( X4 @ ( cP @ ( esk4_1 @ X4 ) @ ( esk5_1 @ X4 ) ) )
| ~ ( X4 @ ( cP @ cZ @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X35: a > a,X36: a > a] :
( ( ( X35
@ ( cP
@ ( esk4_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( X36 @ Z0 ) ) )
@ ( esk5_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( X36 @ Z0 ) ) ) ) )
= ( X36
@ ( cP
@ ( esk4_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( X36 @ Z0 ) ) )
@ ( esk5_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( X36 @ Z0 ) ) ) ) ) )
| ( ( X35 @ ( cP @ cZ @ esk3_0 ) )
!= ( X36 @ ( cP @ cZ @ esk3_0 ) ) ) ),
inference(primitive_enumeration,[status(thm)],[inference(cn,[status(thm)],[]),c_0_4]) ).
thf(c_0_6,negated_conjecture,
! [X2: a,X1: a] :
( ( cL @ ( cP @ X1 @ X2 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X35: a > a] :
( ( ( X35
@ ( cP
@ ( esk4_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( cL @ Z0 ) ) )
@ ( esk5_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( cL @ Z0 ) ) ) ) )
= ( esk4_1
@ ^ [Z0: a] :
( ( X35 @ Z0 )
= ( cL @ Z0 ) ) ) )
| ( ( X35 @ ( cP @ cZ @ esk3_0 ) )
!= cZ ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X4: a > $o] :
( ( ( esk4_1 @ X4 )
!= cZ )
| ~ ( X4 @ ( cP @ ( cL @ ( esk4_1 @ X4 ) ) @ ( cL @ ( esk5_1 @ X4 ) ) ) )
| ~ ( X4 @ ( cP @ ( cR @ ( esk4_1 @ X4 ) ) @ ( cR @ ( esk5_1 @ X4 ) ) ) )
| ~ ( X4 @ ( cP @ cZ @ esk3_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
( ( esk4_1
@ ^ [Z0: a] :
( cZ
= ( cL @ Z0 ) ) )
= cZ ),
inference(er,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
( ( cR @ cZ )
= cZ ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_11,negated_conjecture,
( ( cL @ cZ )
= cZ ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])]),c_0_10]),c_0_6]),c_0_11]),c_0_6]),c_0_6])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU972^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.18 % Computer : n020.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Sep 29 14:55:34 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.23 Running higher-order theorem proving
% 0.12/0.24 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.PvzQxa6QTn/E---3.1_1153905.p
% 0.12/0.28 % Version: 3.5.1-ho
% 0.12/0.28 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting post_as_ho1 with 1500s (5) cores
% 0.12/0.28 % Starting post_as_ho12 with 300s (1) cores
% 0.12/0.28 % Starting new_ho_3 with 300s (1) cores
% 0.12/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.12/0.28 % post_as_ho12 with pid 1153920 completed with status 0
% 0.12/0.28 % Result found by post_as_ho12
% 0.12/0.28 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting post_as_ho1 with 1500s (5) cores
% 0.12/0.28 % Starting post_as_ho12 with 300s (1) cores
% 0.12/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.28 % No SInE strategy applied
% 0.12/0.28 % Search class: HGHSS-FFSF21-MSSFFMBN
% 0.12/0.28 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.28 % SubtermCWHack with pid 1153925 completed with status 10
% 0.12/0.28 % Starting post_as_ho12 with 150s (1) cores
% 0.12/0.28 % post_as_ho12 with pid 1153931 completed with status 0
% 0.12/0.28 % Result found by post_as_ho12
% 0.12/0.28 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.12/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.28 % Starting post_as_ho1 with 1500s (5) cores
% 0.12/0.28 % Starting post_as_ho12 with 300s (1) cores
% 0.12/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.28 % No SInE strategy applied
% 0.12/0.28 % Search class: HGHSS-FFSF21-MSSFFMBN
% 0.12/0.28 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.28 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.28 % SubtermCWHack with pid 1153925 completed with status 10
% 0.12/0.28 % Starting post_as_ho12 with 150s (1) cores
% 0.12/0.28 % Preprocessing time : 0.001 s
% 0.12/0.28 % Presaturation interreduction done
% 0.12/0.28
% 0.12/0.28 % Proof found!
% 0.12/0.28 % SZS status Theorem
% 0.12/0.28 % SZS output start CNFRefutation
% See solution above
% 0.12/0.28 % Parsed axioms : 6
% 0.12/0.28 % Removed by relevancy pruning/SinE : 0
% 0.12/0.28 % Initial clauses : 17
% 0.12/0.28 % Removed in clause preprocessing : 5
% 0.12/0.28 % Initial clauses in saturation : 12
% 0.12/0.28 % Processed clauses : 37
% 0.12/0.28 % ...of these trivial : 1
% 0.12/0.28 % ...subsumed : 1
% 0.12/0.28 % ...remaining for further processing : 35
% 0.12/0.28 % Other redundant clauses eliminated : 17
% 0.12/0.28 % Clauses deleted for lack of memory : 0
% 0.12/0.28 % Backward-subsumed : 1
% 0.12/0.28 % Backward-rewritten : 0
% 0.12/0.28 % Generated clauses : 130
% 0.12/0.28 % ...of the previous two non-redundant : 92
% 0.12/0.28 % ...aggressively subsumed : 0
% 0.12/0.28 % Contextual simplify-reflections : 0
% 0.12/0.28 % Paramodulations : 76
% 0.12/0.28 % Factorizations : 10
% 0.12/0.28 % NegExts : 0
% 0.12/0.28 % Equation resolutions : 26
% 0.12/0.28 % Disequality decompositions : 0
% 0.12/0.28 % Total rewrite steps : 20
% 0.12/0.28 % ...of those cached : 6
% 0.12/0.28 % Propositional unsat checks : 0
% 0.12/0.28 % Propositional check models : 0
% 0.12/0.28 % Propositional check unsatisfiable : 0
% 0.12/0.28 % Propositional clauses : 0
% 0.12/0.28 % Propositional clauses after purity: 0
% 0.12/0.28 % Propositional unsat core size : 0
% 0.12/0.28 % Propositional preprocessing time : 0.000
% 0.12/0.28 % Propositional encoding time : 0.000
% 0.12/0.28 % Propositional solver time : 0.000
% 0.12/0.28 % Success case prop preproc time : 0.000
% 0.12/0.28 % Success case prop encoding time : 0.000
% 0.12/0.28 % Success case prop solver time : 0.000
% 0.12/0.28 % Current number of processed clauses : 21
% 0.12/0.28 % Positive orientable unit clauses : 6
% 0.12/0.28 % Positive unorientable unit clauses: 0
% 0.12/0.28 % Negative unit clauses : 2
% 0.12/0.28 % Non-unit-clauses : 13
% 0.12/0.28 % Current number of unprocessed clauses: 8
% 0.12/0.28 % ...number of literals in the above : 27
% 0.12/0.28 % Current number of archived formulas : 0
% 0.12/0.28 % Current number of archived clauses : 13
% 0.12/0.28 % Clause-clause subsumption calls (NU) : 31
% 0.12/0.28 % Rec. Clause-clause subsumption calls : 12
% 0.12/0.28 % Non-unit clause-clause subsumptions : 2
% 0.12/0.28 % Unit Clause-clause subsumption calls : 3
% 0.12/0.28 % Rewrite failures with RHS unbound : 0
% 0.12/0.28 % BW rewrite match attempts : 0
% 0.12/0.28 % BW rewrite match successes : 0
% 0.12/0.28 % Condensation attempts : 0
% 0.12/0.28 % Condensation successes : 0
% 0.12/0.28 % Termbank termtop insertions : 11403
% 0.12/0.28 % Search garbage collected termcells : 506
% 0.12/0.28
% 0.12/0.28 % -------------------------------------------------
% 0.12/0.28 % User time : 0.006 s
% 0.12/0.28 % System time : 0.005 s
% 0.12/0.28 % Total time : 0.011 s
% 0.12/0.28 % Maximum resident set size: 3640 pages
% 0.12/0.28
% 0.12/0.28 % -------------------------------------------------
% 0.12/0.28 % User time : 0.007 s
% 0.12/0.28 % System time : 0.011 s
% 0.12/0.28 % Total time : 0.018 s
% 0.12/0.28 % Maximum resident set size: 4608 pages
% 0.12/0.28 % E exiting
%------------------------------------------------------------------------------