%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO109^5 : 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 : n012.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 08:42:23 AM UTC 2026
% Result : Theorem 0.08s 0.14s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 0 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 207 ( 11 ~; 44 |; 9 &; 137 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 ^; 37 !; 4 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cP: $i > $o ).
thf(decl_24,type,
cN: $i > $i > $o ).
thf(decl_25,type,
cM: $i > $i > $o ).
thf(decl_26,type,
esk1_0: $i ).
thf(decl_27,type,
esk2_1: $i > $i ).
thf(decl_28,type,
esk3_0: $i ).
thf(cTHM271,conjecture,
( ( ! [X1: $i] :
( ? [X2: $i] :
( ( cM @ X1 @ X2 )
| ( cN @ X1 @ X2 ) )
=> ( cP @ X1 ) )
& ! [X3: $i] :
? [X4: $i] :
( ! [X5: $i] : ( cM @ X4 @ X5 )
| ( cN @ X4 @ X3 ) )
& ! [X3: $i,X6: $i] :
( ( ( cM @ X3 @ X6 )
| ( cN @ X3 @ X6 ) )
=> ( ( cM @ X6 @ X3 )
| ( cN @ X6 @ X3 )
| ( cM @ X6 @ X6 )
| ( cN @ X6 @ X6 ) ) ) )
=> ! [X6: $i] : ( cP @ X6 ) ),
file('/export/starexec/sandbox/tmp/tmp.Xz9P4clu4g/E---3.1_327486.p',cTHM271) ).
thf(c_0_1,negated_conjecture,
~ ( ( ! [X1: $i] :
( ? [X2: $i] :
( ( cM @ X1 @ X2 )
| ( cN @ X1 @ X2 ) )
=> ( cP @ X1 ) )
& ! [X3: $i] :
? [X4: $i] :
( ! [X5: $i] : ( cM @ X4 @ X5 )
| ( cN @ X4 @ X3 ) )
& ! [X3: $i,X6: $i] :
( ( ( cM @ X3 @ X6 )
| ( cN @ X3 @ X6 ) )
=> ( ( cM @ X6 @ X3 )
| ( cN @ X6 @ X3 )
| ( cM @ X6 @ X6 )
| ( cN @ X6 @ X6 ) ) ) )
=> ! [X6: $i] : ( cP @ X6 ) ),
inference(assume_negation,[status(cth)],[cTHM271]) ).
thf(c_0_2,negated_conjecture,
! [X15: $i,X16: $i,X18: $i,X19: $i,X21: $i,X22: $i] :
( ( ~ ( cM @ X15 @ X16 )
| ( cP @ X15 ) )
& ( ~ ( cN @ X15 @ X16 )
| ( cP @ X15 ) )
& ( ( cM @ esk1_0 @ X18 )
| ( cN @ ( esk2_1 @ X19 ) @ X19 ) )
& ( ~ ( cM @ X21 @ X22 )
| ( cM @ X22 @ X21 )
| ( cN @ X22 @ X21 )
| ( cM @ X22 @ X22 )
| ( cN @ X22 @ X22 ) )
& ( ~ ( cN @ X21 @ X22 )
| ( cM @ X22 @ X21 )
| ( cN @ X22 @ X21 )
| ( cM @ X22 @ X22 )
| ( cN @ X22 @ X22 ) )
& ~ ( cP @ 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(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cM @ X2 @ X1 )
| ( cN @ X2 @ X1 )
| ( cM @ X2 @ X2 )
| ( cN @ X2 @ X2 )
| ~ ( cM @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cM @ esk1_0 @ X1 )
| ( cN @ ( esk2_1 @ X2 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP @ X1 )
| ~ ( cN @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cN @ ( esk2_1 @ X1 ) @ X1 )
| ( cN @ X2 @ esk1_0 )
| ( cM @ X2 @ esk1_0 )
| ( cN @ X2 @ X2 )
| ( cM @ X2 @ X2 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP @ X1 )
| ~ ( cM @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cM @ X2 @ X1 )
| ( cN @ X2 @ X1 )
| ( cM @ X2 @ X2 )
| ( cN @ X2 @ X2 )
| ~ ( cN @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cN @ ( esk2_1 @ X1 ) @ X1 )
| ( cP @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),c_0_7]),c_0_5]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cN @ X1 @ ( esk2_1 @ X1 ) )
| ( cM @ X1 @ ( esk2_1 @ X1 ) )
| ( cN @ X1 @ X1 )
| ( cM @ X1 @ X1 )
| ( cP @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cP @ X1 )
| ( cP @ X2 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_10]),c_0_7]),c_0_5]),c_0_7]) ).
thf(c_0_12,negated_conjecture,
~ ( cP @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i] : ( cP @ X1 ),
inference(ef,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO109^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 16:33:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 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.Xz9P4clu4g/E---3.1_327486.p
% 0.08/0.14 % Version: 3.5.1-ho
% 0.08/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.14 % Starting sh4l with 300s (1) cores
% 0.08/0.14 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.14 % ho_unfolding_6 with pid 327519 completed with status 0
% 0.08/0.14 % Result found by ho_unfolding_6
% 0.08/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HGUNF-FFSF11-SFFFFFNN
% 0.08/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.14 % SubtermCWHack with pid 327523 completed with status 0
% 0.08/0.14 % Result found by SubtermCWHack
% 0.08/0.14 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.14 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HGUNF-FFSF11-SFFFFFNN
% 0.08/0.14 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.14 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.14 % Preprocessing time : 0.001 s
% 0.08/0.14
% 0.08/0.14 % Proof found!
% 0.08/0.14 % SZS status Theorem
% 0.08/0.14 % SZS output start CNFRefutation
% See solution above
% 0.08/0.14 % Parsed axioms : 4
% 0.08/0.14 % Removed by relevancy pruning/SinE : 0
% 0.08/0.14 % Initial clauses : 9
% 0.08/0.14 % Removed in clause preprocessing : 3
% 0.08/0.14 % Initial clauses in saturation : 6
% 0.08/0.14 % Processed clauses : 24
% 0.08/0.14 % ...of these trivial : 0
% 0.08/0.14 % ...subsumed : 3
% 0.08/0.14 % ...remaining for further processing : 21
% 0.08/0.14 % Other redundant clauses eliminated : 0
% 0.08/0.14 % Clauses deleted for lack of memory : 0
% 0.08/0.14 % Backward-subsumed : 8
% 0.08/0.14 % Backward-rewritten : 7
% 0.08/0.14 % Generated clauses : 37
% 0.08/0.14 % ...of the previous two non-redundant : 34
% 0.08/0.14 % ...aggressively subsumed : 0
% 0.08/0.14 % Contextual simplify-reflections : 12
% 0.08/0.14 % Paramodulations : 31
% 0.08/0.14 % Factorizations : 6
% 0.08/0.14 % NegExts : 0
% 0.08/0.14 % Equation resolutions : 0
% 0.08/0.14 % Disequality decompositions : 0
% 0.08/0.14 % Total rewrite steps : 10
% 0.08/0.14 % ...of those cached : 2
% 0.08/0.14 % Propositional unsat checks : 0
% 0.08/0.14 % Propositional check models : 0
% 0.08/0.14 % Propositional check unsatisfiable : 0
% 0.08/0.14 % Propositional clauses : 0
% 0.08/0.14 % Propositional clauses after purity: 0
% 0.08/0.14 % Propositional unsat core size : 0
% 0.08/0.14 % Propositional preprocessing time : 0.000
% 0.08/0.14 % Propositional encoding time : 0.000
% 0.08/0.14 % Propositional solver time : 0.000
% 0.08/0.14 % Success case prop preproc time : 0.000
% 0.08/0.14 % Success case prop encoding time : 0.000
% 0.08/0.14 % Success case prop solver time : 0.000
% 0.08/0.14 % Current number of processed clauses : 6
% 0.08/0.14 % Positive orientable unit clauses : 1
% 0.08/0.14 % Positive unorientable unit clauses: 0
% 0.08/0.14 % Negative unit clauses : 0
% 0.08/0.14 % Non-unit-clauses : 5
% 0.08/0.14 % Current number of unprocessed clauses: 11
% 0.08/0.14 % ...number of literals in the above : 64
% 0.08/0.14 % Current number of archived formulas : 0
% 0.08/0.14 % Current number of archived clauses : 15
% 0.08/0.14 % Clause-clause subsumption calls (NU) : 94
% 0.08/0.14 % Rec. Clause-clause subsumption calls : 35
% 0.08/0.14 % Non-unit clause-clause subsumptions : 16
% 0.08/0.14 % Unit Clause-clause subsumption calls : 8
% 0.08/0.14 % Rewrite failures with RHS unbound : 0
% 0.08/0.14 % BW rewrite match attempts : 8
% 0.08/0.14 % BW rewrite match successes : 8
% 0.08/0.14 % Condensation attempts : 0
% 0.08/0.14 % Condensation successes : 0
% 0.08/0.14 % Termbank termtop insertions : 1298
% 0.08/0.14 % Search garbage collected termcells : 257
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.004 s
% 0.08/0.14 % System time : 0.000 s
% 0.08/0.14 % Total time : 0.004 s
% 0.08/0.14 % Maximum resident set size: 3632 pages
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.007 s
% 0.08/0.14 % System time : 0.000 s
% 0.08/0.14 % Total time : 0.007 s
% 0.08/0.14 % Maximum resident set size: 4864 pages
% 0.08/0.14 % E exiting
%------------------------------------------------------------------------------