%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV204^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:35:12 AM UTC 2026
% Result : Theorem 0.24s 0.38s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 52 equ; 0 cnn)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 449 ( 39 ~; 42 |; 46 &; 304 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 11 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 121 ( 12 ^; 91 !; 18 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
iS: $tType ).
thf(decl_23,type,
y: iS ).
thf(decl_24,type,
x: iS ).
thf(decl_25,type,
cP: iS > iS > iS ).
thf(decl_26,type,
c0: iS ).
thf(decl_27,type,
esk1_1: ( iS > $o ) > iS ).
thf(decl_28,type,
esk2_1: ( iS > $o ) > iS ).
thf(decl_29,type,
epred1_0: iS > iS > iS > $o ).
thf(cS_INCL_LEM4_pme,conjecture,
( ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
& ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ( ( X1 = X2 )
& ( X3 = X4 ) ) )
& ! [X5: iS > $o] :
( ( ( X5 @ c0 )
& ! [X1: iS,X2: iS] :
( ( ( X5 @ X1 )
& ( X5 @ X2 ) )
=> ( X5 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X1: iS] : ( X5 @ X1 ) ) )
=> ! [X6: iS > iS > iS > $o] :
( ( $true
& ! [X7: iS,X8: iS,X9: iS] :
( ( ( ( X7 = c0 )
& ( X8 = X9 ) )
| ( ( X8 = c0 )
& ( X7 = X9 ) )
| ? [X10: iS,X11: iS,X12: iS,X13: iS,X14: iS,X15: iS] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nG1caHkrXR/E---3.1_1795908.p',cS_INCL_LEM4_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
& ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ( ( X1 = X2 )
& ( X3 = X4 ) ) )
& ! [X5: iS > $o] :
( ( ( X5 @ c0 )
& ! [X1: iS,X2: iS] :
( ( ( X5 @ X1 )
& ( X5 @ X2 ) )
=> ( X5 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X1: iS] : ( X5 @ X1 ) ) )
=> ! [X6: iS > iS > iS > $o] :
( ( $true
& ! [X7: iS,X8: iS,X9: iS] :
( ( ( ( X7 = c0 )
& ( X8 = X9 ) )
| ( ( X8 = c0 )
& ( X7 = X9 ) )
| ? [X10: iS,X11: iS,X12: iS,X13: iS,X14: iS,X15: iS] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(assume_negation,[status(cth)],[cS_INCL_LEM4_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( ! [X1: iS,X2: iS] :
( ( cP @ X1 @ X2 )
!= c0 )
& ! [X1: iS,X2: iS,X3: iS,X4: iS] :
( ( ( cP @ X1 @ X3 )
= ( cP @ X2 @ X4 ) )
=> ( ( X1 = X2 )
& ( X3 = X4 ) ) )
& ! [X5: iS > $o] :
( ( ( X5 @ c0 )
& ! [X1: iS,X2: iS] :
( ( ( X5 @ X1 )
& ( X5 @ X2 ) )
=> ( X5 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X1: iS] : ( X5 @ X1 ) ) )
=> ! [X6: iS > iS > iS > $o] :
( ( $true
& ! [X7: iS,X8: iS,X9: iS] :
( ( ( ( X7 = c0 )
& ( X8 = X9 ) )
| ( ( X8 = c0 )
& ( X7 = X9 ) )
| ? [X10: iS,X11: iS,X12: iS,X13: iS,X14: iS,X15: iS] :
( ( X7
= ( cP @ X10 @ X11 ) )
& ( X8
= ( cP @ X12 @ X13 ) )
& ( X9
= ( cP @ X14 @ X15 ) )
& ( X6 @ X10 @ X12 @ X14 )
& ( X6 @ X11 @ X13 @ X15 ) ) )
=> ( X6 @ X7 @ X8 @ X9 ) ) )
=> ( X6 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
thf(c_0_3,negated_conjecture,
! [X36: iS,X37: iS,X38: iS,X39: iS,X40: iS,X41: iS,X42: iS > $o,X45: iS,X47: iS,X48: iS,X49: iS,X50: iS,X51: iS,X52: iS,X53: iS,X54: iS,X55: iS] :
( ( ( cP @ X36 @ X37 )
!= c0 )
& ( ( X38 = X39 )
| ( ( cP @ X38 @ X40 )
!= ( cP @ X39 @ X41 ) ) )
& ( ( X40 = X41 )
| ( ( cP @ X38 @ X40 )
!= ( cP @ X39 @ X41 ) ) )
& ( ( X42 @ ( esk1_1 @ X42 ) )
| ~ ( X42 @ c0 )
| ( X42 @ X45 ) )
& ( ( X42 @ ( esk2_1 @ X42 ) )
| ~ ( X42 @ c0 )
| ( X42 @ X45 ) )
& ( ~ ( X42 @ ( cP @ ( esk1_1 @ X42 ) @ ( esk2_1 @ X42 ) ) )
| ~ ( X42 @ c0 )
| ( X42 @ X45 ) )
& $true
& ( ( X47 != c0 )
| ( X48 != X49 )
| ( epred1_0 @ X47 @ X48 @ X49 ) )
& ( ( X48 != c0 )
| ( X47 != X49 )
| ( epred1_0 @ X47 @ X48 @ X49 ) )
& ( ( X47
!= ( cP @ X50 @ X51 ) )
| ( X48
!= ( cP @ X52 @ X53 ) )
| ( X49
!= ( cP @ X54 @ X55 ) )
| ~ ( epred1_0 @ X50 @ X52 @ X54 )
| ~ ( epred1_0 @ X51 @ X53 @ X55 )
| ( epred1_0 @ X47 @ X48 @ X49 ) )
& ~ ( epred1_0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ) ),
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: iS,X2: iS,X3: iS] :
( ( epred1_0 @ X1 @ X2 @ X3 )
| ( X1 != c0 )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X1: iS,X5: iS > $o] :
( ( X5 @ ( esk2_1 @ X5 ) )
| ( X5 @ X1 )
| ~ ( X5 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_6,negated_conjecture,
! [X1: iS] : ( epred1_0 @ c0 @ X1 @ X1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_4])]) ).
thf(c_0_7,negated_conjecture,
! [X1: iS,X5: iS > $o] :
( ( X5 @ ( esk1_1 @ X5 ) )
| ( X5 @ X1 )
| ~ ( X5 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_8,negated_conjecture,
! [X7: iS,X1: iS,X2: iS,X4: iS,X3: iS,X9: iS,X8: iS,X10: iS,X11: iS] :
( ( epred1_0 @ X1 @ X4 @ X9 )
| ( X1
!= ( cP @ X2 @ X3 ) )
| ( X4
!= ( cP @ X7 @ X8 ) )
| ( X9
!= ( cP @ X10 @ X11 ) )
| ~ ( epred1_0 @ X2 @ X7 @ X10 )
| ~ ( epred1_0 @ X3 @ X8 @ X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X1: iS,X2: iS,X3: iS] :
( ( epred1_0 @ X2 @ X1 @ X3 )
| ( X1 != c0 )
| ( X2 != X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_10,negated_conjecture,
! [X1: iS] :
( ( epred1_0
@ ( esk2_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk2_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk2_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) ) )
| ( epred1_0 @ X1 @ X1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: iS] :
( ( epred1_0
@ ( esk1_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk1_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk1_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) ) )
| ( epred1_0 @ X1 @ X1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
thf(c_0_12,negated_conjecture,
~ ( epred1_0 @ ( cP @ x @ c0 ) @ ( cP @ x @ y ) @ ( cP @ x @ y ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_13,negated_conjecture,
! [X2: iS,X8: iS,X4: iS,X3: iS,X1: iS,X7: iS] :
( ( epred1_0 @ ( cP @ X1 @ X2 ) @ ( cP @ X3 @ X4 ) @ ( cP @ X7 @ X8 ) )
| ~ ( epred1_0 @ X2 @ X4 @ X8 )
| ~ ( epred1_0 @ X1 @ X3 @ X7 ) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8])])]) ).
thf(c_0_14,negated_conjecture,
! [X1: iS,X5: iS > $o] :
( ( X5 @ X1 )
| ~ ( X5 @ ( cP @ ( esk1_1 @ X5 ) @ ( esk2_1 @ X5 ) ) )
| ~ ( X5 @ c0 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_15,negated_conjecture,
! [X1: iS] : ( epred1_0 @ X1 @ c0 @ X1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
thf(c_0_16,negated_conjecture,
( epred1_0
@ ( esk2_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk2_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk2_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) ) ),
inference(ef,[status(thm)],[c_0_10]) ).
thf(c_0_17,negated_conjecture,
( epred1_0
@ ( esk1_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk1_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) )
@ ( esk1_1
@ ^ [Z0: iS] : ( epred1_0 @ Z0 @ Z0 @ Z0 ) ) ),
inference(ef,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
~ ( epred1_0 @ x @ x @ x ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_6])]) ).
thf(c_0_19,negated_conjecture,
! [X1: iS] : ( epred1_0 @ X1 @ X1 @ X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15])]),c_0_16]),c_0_17])]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV204^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 % Computer : n005.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8046.5625MB
% 0.08/0.25 % OS : Linux 6.8.0-71-generic
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Sep 29 15:20:46 UTC 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.31 Running higher-order theorem proving
% 0.24/0.33 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.nG1caHkrXR/E---3.1_1795908.p
% 0.24/0.38 % Version: 3.5.1-ho
% 0.24/0.38 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.24/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.38 % Starting post_as_ho1 with 1500s (5) cores
% 0.24/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.24/0.38 % Starting new_ho_3 with 300s (1) cores
% 0.24/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.24/0.38 % post_as_ho12 with pid 1795922 completed with status 0
% 0.24/0.38 % Result found by post_as_ho12
% 0.24/0.38 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.24/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.38 % Starting post_as_ho1 with 1500s (5) cores
% 0.24/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.24/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.38 % No SInE strategy applied
% 0.24/0.38 % Search class: HGUSF-FFSF21-SSSFFSBN
% 0.24/0.38 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.38 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.38 % SubtermCWHack with pid 1795931 completed with status 10
% 0.24/0.38 % Starting post_as_ho12 with 181s (1) cores
% 0.24/0.38 % post_as_ho12 with pid 1795936 completed with status 0
% 0.24/0.38 % Result found by post_as_ho12
% 0.24/0.38 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.24/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.38 % Starting post_as_ho1 with 1500s (5) cores
% 0.24/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.24/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.38 % No SInE strategy applied
% 0.24/0.38 % Search class: HGUSF-FFSF21-SSSFFSBN
% 0.24/0.38 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.38 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.38 % SubtermCWHack with pid 1795931 completed with status 10
% 0.24/0.38 % Starting post_as_ho12 with 181s (1) cores
% 0.24/0.38 % Preprocessing time : 0.001 s
% 0.24/0.38 % Presaturation interreduction done
% 0.24/0.38
% 0.24/0.38 % Proof found!
% 0.24/0.38 % SZS status Theorem
% 0.24/0.38 % SZS output start CNFRefutation
% See solution above
% 0.24/0.38 % Parsed axioms : 6
% 0.24/0.38 % Removed by relevancy pruning/SinE : 0
% 0.24/0.38 % Initial clauses : 16
% 0.24/0.38 % Removed in clause preprocessing : 6
% 0.24/0.38 % Initial clauses in saturation : 10
% 0.24/0.38 % Processed clauses : 70
% 0.24/0.38 % ...of these trivial : 5
% 0.24/0.38 % ...subsumed : 13
% 0.24/0.38 % ...remaining for further processing : 52
% 0.24/0.38 % Other redundant clauses eliminated : 43
% 0.24/0.38 % Clauses deleted for lack of memory : 0
% 0.24/0.38 % Backward-subsumed : 10
% 0.24/0.38 % Backward-rewritten : 4
% 0.24/0.38 % Generated clauses : 330
% 0.24/0.38 % ...of the previous two non-redundant : 240
% 0.24/0.38 % ...aggressively subsumed : 0
% 0.24/0.38 % Contextual simplify-reflections : 0
% 0.24/0.38 % Paramodulations : 225
% 0.24/0.38 % Factorizations : 24
% 0.24/0.38 % NegExts : 0
% 0.24/0.38 % Equation resolutions : 70
% 0.24/0.38 % Disequality decompositions : 0
% 0.24/0.38 % Total rewrite steps : 42
% 0.24/0.38 % ...of those cached : 24
% 0.24/0.38 % Propositional unsat checks : 0
% 0.24/0.38 % Propositional check models : 0
% 0.24/0.38 % Propositional check unsatisfiable : 0
% 0.24/0.38 % Propositional clauses : 0
% 0.24/0.38 % Propositional clauses after purity: 0
% 0.24/0.38 % Propositional unsat core size : 0
% 0.24/0.38 % Propositional preprocessing time : 0.000
% 0.24/0.38 % Propositional encoding time : 0.000
% 0.24/0.38 % Propositional solver time : 0.000
% 0.24/0.38 % Success case prop preproc time : 0.000
% 0.24/0.38 % Success case prop encoding time : 0.000
% 0.24/0.38 % Success case prop solver time : 0.000
% 0.24/0.38 % Current number of processed clauses : 25
% 0.24/0.38 % Positive orientable unit clauses : 11
% 0.24/0.38 % Positive unorientable unit clauses: 0
% 0.24/0.38 % Negative unit clauses : 2
% 0.24/0.38 % Non-unit-clauses : 12
% 0.24/0.38 % Current number of unprocessed clauses: 39
% 0.24/0.38 % ...number of literals in the above : 117
% 0.24/0.38 % Current number of archived formulas : 0
% 0.24/0.38 % Current number of archived clauses : 24
% 0.24/0.38 % Clause-clause subsumption calls (NU) : 54
% 0.24/0.38 % Rec. Clause-clause subsumption calls : 39
% 0.24/0.38 % Non-unit clause-clause subsumptions : 3
% 0.24/0.38 % Unit Clause-clause subsumption calls : 17
% 0.24/0.38 % Rewrite failures with RHS unbound : 0
% 0.24/0.38 % BW rewrite match attempts : 23
% 0.24/0.38 % BW rewrite match successes : 13
% 0.24/0.38 % Condensation attempts : 0
% 0.24/0.38 % Condensation successes : 0
% 0.24/0.38 % Termbank termtop insertions : 22032
% 0.24/0.38 % Search garbage collected termcells : 578
% 0.24/0.38
% 0.24/0.38 % -------------------------------------------------
% 0.24/0.38 % User time : 0.017 s
% 0.24/0.38 % System time : 0.005 s
% 0.24/0.38 % Total time : 0.022 s
% 0.24/0.38 % Maximum resident set size: 3648 pages
% 0.24/0.38
% 0.24/0.38 % -------------------------------------------------
% 0.24/0.38 % User time : 0.017 s
% 0.24/0.38 % System time : 0.011 s
% 0.24/0.38 % Total time : 0.028 s
% 0.24/0.38 % Maximum resident set size: 4608 pages
% 0.24/0.38 % E exiting
%------------------------------------------------------------------------------