%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV045^5 : 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 : 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 08:34:46 AM UTC 2026
% Result : Theorem 0.23s 0.27s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 5 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 353 ( 29 ~; 25 |; 18 &; 254 @)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_sort2,type,
b: $tType ).
thf(decl_23,type,
g: a > b ).
thf(decl_24,type,
f: a > b ).
thf(decl_25,type,
cQ: a > b > b > $o ).
thf(decl_26,type,
cP: a > a > $o ).
thf(decl_27,type,
esk1_0: a ).
thf(decl_28,type,
esk2_0: a ).
thf(cTHM509_pme,conjecture,
( ! [X1: a] :
( ( cP @ X1 @ X1 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X1 ) ) )
=> ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) )
=> ( ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cP @ X2 @ X1 ) )
& ! [X1: a,X2: a,X3: a] :
( ( ( cP @ X1 @ X2 )
& ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) )
=> ( ( ! [X1: a] :
( ( cP @ X1 @ X1 )
=> ( ! [X4: b,X5: b] :
( ( cQ @ X1 @ X4 @ X5 )
=> ( cQ @ X1 @ X5 @ X4 ) )
& ! [X4: b,X6: b,X7: b] :
( ( ( cQ @ X1 @ X4 @ X6 )
& ( cQ @ X1 @ X6 @ X7 ) )
=> ( cQ @ X1 @ X4 @ X7 ) ) ) )
& ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vaH5GcHTSV/E---3.1_1404202.p',cTHM509_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ! [X1: a] :
( ( cP @ X1 @ X1 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X1 ) ) )
=> ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) ) )
=> ( ( ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cP @ X2 @ X1 ) )
& ! [X1: a,X2: a,X3: a] :
( ( ( cP @ X1 @ X2 )
& ( cP @ X2 @ X3 ) )
=> ( cP @ X1 @ X3 ) ) )
=> ( ( ! [X1: a] :
( ( cP @ X1 @ X1 )
=> ( ! [X4: b,X5: b] :
( ( cQ @ X1 @ X4 @ X5 )
=> ( cQ @ X1 @ X5 @ X4 ) )
& ! [X4: b,X6: b,X7: b] :
( ( ( cQ @ X1 @ X4 @ X6 )
& ( cQ @ X1 @ X6 @ X7 ) )
=> ( cQ @ X1 @ X4 @ X7 ) ) ) )
& ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( ( cQ @ X1 )
= ( cQ @ X2 ) ) ) )
=> ! [X1: a,X2: a] :
( ( cP @ X1 @ X2 )
=> ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X2 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM509_pme]) ).
thf(c_0_2,negated_conjecture,
! [X26: a,X27: a,X28: a,X29: a,X30: a,X31: a,X32: a,X33: a,X34: a,X35: b,X36: b,X37: b,X38: b,X39: b,X40: a,X41: a] :
( ( ~ ( cP @ X26 @ X26 )
| ( cQ @ X26 @ ( f @ X26 ) @ ( g @ X26 ) ) )
& ( ~ ( cP @ X27 @ X28 )
| ( cQ @ X27 @ ( f @ X27 ) @ ( f @ X28 ) ) )
& ( ~ ( cP @ X29 @ X30 )
| ( cP @ X30 @ X29 ) )
& ( ~ ( cP @ X31 @ X32 )
| ~ ( cP @ X32 @ X33 )
| ( cP @ X31 @ X33 ) )
& ( ~ ( cQ @ X34 @ X35 @ X36 )
| ( cQ @ X34 @ X36 @ X35 )
| ~ ( cP @ X34 @ X34 ) )
& ( ~ ( cQ @ X34 @ X37 @ X38 )
| ~ ( cQ @ X34 @ X38 @ X39 )
| ( cQ @ X34 @ X37 @ X39 )
| ~ ( cP @ X34 @ X34 ) )
& ( ~ ( cP @ X40 @ X41 )
| ( ( cQ @ X40 )
= ( cQ @ X41 ) ) )
& ( cP @ esk1_0 @ esk2_0 )
& ~ ( cQ @ esk1_0 @ ( f @ esk1_0 ) @ ( g @ esk2_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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: a,X2: a] :
( ( cP @ X2 @ X1 )
| ~ ( cP @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
cP @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X1: a,X2: a] :
( ( ( cQ @ X1 )
= ( cQ @ X2 ) )
| ~ ( cP @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
cP @ esk2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_7,negated_conjecture,
! [X1: a,X2: a,X3: a] :
( ( cP @ X1 @ X3 )
| ~ ( cP @ X1 @ X2 )
| ~ ( cP @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
( ( cQ @ esk2_0 )
= ( cQ @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: a] :
( ( cP @ X1 @ esk2_0 )
| ~ ( cP @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
thf(c_0_10,negated_conjecture,
! [X46: b,X47: b] :
( ( cQ @ esk2_0 @ X46 @ X47 )
<=> ( cQ @ esk1_0 @ X46 @ X47 ) ),
inference(arg_cong,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: a] :
( ( cP @ esk2_0 @ X1 )
| ~ ( cP @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X4: b,X5: b] :
( ( cQ @ esk1_0 @ X4 @ X5 )
| ~ ( cQ @ esk2_0 @ X4 @ X5 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: a] :
( ( cQ @ X1 @ ( f @ X1 ) @ ( g @ X1 ) )
| ~ ( cP @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_14,negated_conjecture,
cP @ esk2_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
thf(c_0_15,negated_conjecture,
! [X1: a] :
( ( cP @ X1 @ esk1_0 )
| ~ ( cP @ X1 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
thf(c_0_16,negated_conjecture,
! [X4: b,X6: b,X5: b,X1: a] :
( ( cQ @ X1 @ X4 @ X6 )
| ~ ( cQ @ X1 @ X4 @ X5 )
| ~ ( cQ @ X1 @ X5 @ X6 )
| ~ ( cP @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_17,negated_conjecture,
cQ @ esk1_0 @ ( f @ esk2_0 ) @ ( g @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
thf(c_0_18,negated_conjecture,
cP @ esk1_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_15,c_0_4]) ).
thf(c_0_19,negated_conjecture,
~ ( cQ @ esk1_0 @ ( f @ esk1_0 ) @ ( g @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_20,negated_conjecture,
! [X4: b] :
( ( cQ @ esk1_0 @ X4 @ ( g @ esk2_0 ) )
| ~ ( cQ @ esk1_0 @ X4 @ ( f @ esk2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
thf(c_0_21,negated_conjecture,
~ ( cQ @ esk1_0 @ ( f @ esk1_0 ) @ ( f @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
! [X1: a,X2: a] :
( ( cQ @ X1 @ ( f @ X1 ) @ ( f @ X2 ) )
| ~ ( cP @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_4])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV045^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:05:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 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.vaH5GcHTSV/E---3.1_1404202.p
% 0.23/0.27 % Version: 3.5.1-ho
% 0.23/0.27 % Preprocessing class: HSMSSMSSSSSNSSN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_11 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % Starting new_ho_9 with 300s (1) cores
% 0.23/0.27 % Starting ho_unfolding_4 with 300s (1) cores
% 0.23/0.27 % sh5l with pid 1404232 completed with status 0
% 0.23/0.27 % Result found by sh5l
% 0.23/0.27 % Preprocessing class: HSMSSMSSSSSNSSN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_11 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.27 % Search class: HHUSF-FFSF11-SSSFFFNN
% 0.23/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.27 % SubtermCWHack with pid 1404238 completed with status 0
% 0.23/0.27 % Result found by SubtermCWHack
% 0.23/0.27 % Preprocessing class: HSMSSMSSSSSNSSN.
% 0.23/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.27 % Starting new_ho_11 with 1500s (5) cores
% 0.23/0.27 % Starting sh5l with 300s (1) cores
% 0.23/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.23/0.27 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.23/0.27 % Search class: HHUSF-FFSF11-SSSFFFNN
% 0.23/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.23/0.27 % Preprocessing time : 0.001 s
% 0.23/0.27
% 0.23/0.27 % Proof found!
% 0.23/0.27 % SZS status Theorem
% 0.23/0.27 % SZS output start CNFRefutation
% See solution above
% 0.23/0.27 % Parsed axioms : 7
% 0.23/0.27 % Removed by relevancy pruning/SinE : 6
% 0.23/0.27 % Initial clauses : 9
% 0.23/0.27 % Removed in clause preprocessing : 0
% 0.23/0.27 % Initial clauses in saturation : 9
% 0.23/0.27 % Processed clauses : 48
% 0.23/0.27 % ...of these trivial : 2
% 0.23/0.27 % ...subsumed : 11
% 0.23/0.27 % ...remaining for further processing : 35
% 0.23/0.27 % Other redundant clauses eliminated : 0
% 0.23/0.27 % Clauses deleted for lack of memory : 0
% 0.23/0.27 % Backward-subsumed : 0
% 0.23/0.27 % Backward-rewritten : 0
% 0.23/0.27 % Generated clauses : 78
% 0.23/0.27 % ...of the previous two non-redundant : 57
% 0.23/0.27 % ...aggressively subsumed : 0
% 0.23/0.27 % Contextual simplify-reflections : 0
% 0.23/0.27 % Paramodulations : 68
% 0.23/0.27 % Factorizations : 0
% 0.23/0.27 % NegExts : 0
% 0.23/0.27 % Equation resolutions : 0
% 0.23/0.27 % Disequality decompositions : 0
% 0.23/0.27 % Total rewrite steps : 43
% 0.23/0.27 % ...of those cached : 33
% 0.23/0.27 % Propositional unsat checks : 0
% 0.23/0.27 % Propositional check models : 0
% 0.23/0.27 % Propositional check unsatisfiable : 0
% 0.23/0.27 % Propositional clauses : 0
% 0.23/0.27 % Propositional clauses after purity: 0
% 0.23/0.27 % Propositional unsat core size : 0
% 0.23/0.27 % Propositional preprocessing time : 0.000
% 0.23/0.27 % Propositional encoding time : 0.000
% 0.23/0.27 % Propositional solver time : 0.000
% 0.23/0.27 % Success case prop preproc time : 0.000
% 0.23/0.27 % Success case prop encoding time : 0.000
% 0.23/0.27 % Success case prop solver time : 0.000
% 0.23/0.27 % Current number of processed clauses : 33
% 0.23/0.27 % Positive orientable unit clauses : 10
% 0.23/0.27 % Positive unorientable unit clauses: 0
% 0.23/0.27 % Negative unit clauses : 2
% 0.23/0.27 % Non-unit-clauses : 21
% 0.23/0.27 % Current number of unprocessed clauses: 18
% 0.23/0.27 % ...number of literals in the above : 47
% 0.23/0.27 % Current number of archived formulas : 0
% 0.23/0.27 % Current number of archived clauses : 2
% 0.23/0.27 % Clause-clause subsumption calls (NU) : 58
% 0.23/0.27 % Rec. Clause-clause subsumption calls : 57
% 0.23/0.27 % Non-unit clause-clause subsumptions : 11
% 0.23/0.27 % Unit Clause-clause subsumption calls : 0
% 0.23/0.27 % Rewrite failures with RHS unbound : 0
% 0.23/0.27 % BW rewrite match attempts : 2
% 0.23/0.27 % BW rewrite match successes : 0
% 0.23/0.27 % Condensation attempts : 0
% 0.23/0.27 % Condensation successes : 0
% 0.23/0.27 % Termbank termtop insertions : 2255
% 0.23/0.27 % Search garbage collected termcells : 463
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.006 s
% 0.23/0.27 % System time : 0.000 s
% 0.23/0.27 % Total time : 0.006 s
% 0.23/0.27 % Maximum resident set size: 3640 pages
% 0.23/0.27
% 0.23/0.27 % -------------------------------------------------
% 0.23/0.27 % User time : 0.007 s
% 0.23/0.27 % System time : 0.003 s
% 0.23/0.27 % Total time : 0.010 s
% 0.23/0.27 % Maximum resident set size: 4864 pages
% 0.23/0.27 % E exiting
%------------------------------------------------------------------------------