%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEV218^5 : 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 : n002.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 08:35:13 AM UTC 2026
% Result : Theorem 0.28s 0.38s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 34 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 0 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 385 ( 54 ~; 59 |; 19 &; 243 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 43 !; 4 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
a: $tType ).
thf(decl_23,type,
cQ: a > a > $o ).
thf(decl_24,type,
epred1_0: a > a > $o ).
thf(decl_25,type,
esk1_1: a > a ).
thf(decl_26,type,
esk2_0: a ).
thf(decl_27,type,
esk3_0: a ).
thf(decl_28,type,
esk4_0: a ).
thf(decl_29,type,
esk5_0: a ).
thf(decl_30,type,
esk6_0: a ).
thf(decl_31,type,
esk7_0: a ).
thf(cTHM559A_pme,conjecture,
( ? [X1: a > a > $o] :
! [X2: a] :
( ? [X3: a] : ( X1 @ X2 @ X3 )
& ! [X4: a] :
( ( X1 @ X2 @ X4 )
=> ! [X5: a] :
( ( X1 @ X2 @ X5 )
<=> ( cQ @ X4 @ X5 ) ) )
& ( X1 @ X2 @ X2 ) )
=> ( ! [X2: a] : ( cQ @ X2 @ X2 )
& ! [X2: a,X5: a] :
( ( cQ @ X2 @ X5 )
=> ( cQ @ X5 @ X2 ) )
& ! [X2: a,X5: a,X3: a] :
( ( ( cQ @ X2 @ X5 )
& ( cQ @ X5 @ X3 ) )
=> ( cQ @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.l3vryOKJWk/E---3.1_1424865.p',cTHM559A_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ? [X1: a > a > $o] :
! [X2: a] :
( ? [X3: a] : ( X1 @ X2 @ X3 )
& ! [X4: a] :
( ( X1 @ X2 @ X4 )
=> ! [X5: a] :
( ( X1 @ X2 @ X5 )
<=> ( cQ @ X4 @ X5 ) ) )
& ( X1 @ X2 @ X2 ) )
=> ( ! [X2: a] : ( cQ @ X2 @ X2 )
& ! [X2: a,X5: a] :
( ( cQ @ X2 @ X5 )
=> ( cQ @ X5 @ X2 ) )
& ! [X2: a,X5: a,X3: a] :
( ( ( cQ @ X2 @ X5 )
& ( cQ @ X5 @ X3 ) )
=> ( cQ @ X2 @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM559A_pme]) ).
thf(c_0_2,negated_conjecture,
! [X18: a,X20: a,X21: a] :
( ( epred1_0 @ X18 @ ( esk1_1 @ X18 ) )
& ( ~ ( epred1_0 @ X18 @ X21 )
| ( cQ @ X20 @ X21 )
| ~ ( epred1_0 @ X18 @ X20 ) )
& ( ~ ( cQ @ X20 @ X21 )
| ( epred1_0 @ X18 @ X21 )
| ~ ( epred1_0 @ X18 @ X20 ) )
& ( epred1_0 @ X18 @ X18 )
& ( ( cQ @ esk5_0 @ esk6_0 )
| ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) )
& ( ( cQ @ esk6_0 @ esk7_0 )
| ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) )
& ( ~ ( cQ @ esk5_0 @ esk7_0 )
| ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) )
& ( ( cQ @ esk5_0 @ esk6_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) )
& ( ( cQ @ esk6_0 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) )
& ( ~ ( cQ @ esk5_0 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk2_0 @ 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,
! [X2: a,X3: a,X4: a] :
( ( cQ @ X4 @ X3 )
| ~ ( epred1_0 @ X2 @ X3 )
| ~ ( epred1_0 @ X2 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
! [X2: a] : ( epred1_0 @ X2 @ X2 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X2: a,X3: a] :
( ( cQ @ X2 @ X3 )
| ~ ( epred1_0 @ X2 @ X3 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_6,negated_conjecture,
( ( cQ @ esk6_0 @ esk7_0 )
| ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_7,negated_conjecture,
! [X2: a] : ( cQ @ X2 @ X2 ),
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
thf(c_0_8,negated_conjecture,
! [X4: a,X3: a,X2: a] :
( ( epred1_0 @ X4 @ X3 )
| ~ ( cQ @ X2 @ X3 )
| ~ ( epred1_0 @ X4 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_9,negated_conjecture,
( ( cQ @ esk3_0 @ esk4_0 )
| ( cQ @ esk6_0 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).
thf(c_0_10,negated_conjecture,
( ( cQ @ esk5_0 @ esk6_0 )
| ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_11,negated_conjecture,
! [X2: a] :
( ( cQ @ esk3_0 @ esk4_0 )
| ( epred1_0 @ X2 @ esk7_0 )
| ~ ( epred1_0 @ X2 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
( ( cQ @ esk3_0 @ esk4_0 )
| ( cQ @ esk5_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_7])]) ).
thf(c_0_13,negated_conjecture,
! [X2: a] :
( ( cQ @ esk3_0 @ esk4_0 )
| ( cQ @ X2 @ esk7_0 )
| ~ ( epred1_0 @ X2 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X2: a] :
( ( cQ @ esk3_0 @ esk4_0 )
| ( epred1_0 @ X2 @ esk6_0 )
| ~ ( epred1_0 @ X2 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
thf(c_0_15,negated_conjecture,
( ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk5_0 @ esk7_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_16,negated_conjecture,
( ( cQ @ esk6_0 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_17,negated_conjecture,
! [X2: a] :
( ( cQ @ esk3_0 @ esk4_0 )
| ( cQ @ X2 @ esk7_0 )
| ~ ( epred1_0 @ X2 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_18,negated_conjecture,
( ( cQ @ esk3_0 @ esk4_0 )
| ~ ( cQ @ esk5_0 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_7])]) ).
thf(c_0_19,negated_conjecture,
( ( cQ @ esk6_0 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_7])]) ).
thf(c_0_20,negated_conjecture,
( ( cQ @ esk5_0 @ esk6_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_21,negated_conjecture,
cQ @ esk3_0 @ esk4_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_4]),c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X2: a] :
( ( epred1_0 @ X2 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_19]) ).
thf(c_0_23,negated_conjecture,
( ( cQ @ esk5_0 @ esk6_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_7])]) ).
thf(c_0_24,negated_conjecture,
! [X2: a] :
( ( epred1_0 @ X2 @ esk4_0 )
| ~ ( epred1_0 @ X2 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
thf(c_0_25,negated_conjecture,
! [X2: a] :
( ( cQ @ X2 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_5,c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X2: a] :
( ( epred1_0 @ X2 @ esk6_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_23]) ).
thf(c_0_27,negated_conjecture,
( ~ ( cQ @ esk5_0 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_28,negated_conjecture,
! [X3: a,X2: a] :
( ( cQ @ esk4_0 @ X2 )
| ~ ( epred1_0 @ X3 @ esk3_0 )
| ~ ( epred1_0 @ X3 @ X2 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_24]) ).
thf(c_0_29,negated_conjecture,
! [X2: a] :
( ( cQ @ X2 @ esk7_0 )
| ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( epred1_0 @ X2 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,negated_conjecture,
( ~ ( cQ @ esk4_0 @ esk3_0 )
| ~ ( cQ @ esk5_0 @ esk7_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_7])]) ).
thf(c_0_31,negated_conjecture,
! [X2: a] :
( ( cQ @ esk4_0 @ X2 )
| ~ ( epred1_0 @ esk3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_4]) ).
thf(c_0_32,negated_conjecture,
~ ( cQ @ esk4_0 @ esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_4]),c_0_30]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_4]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV218^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n002.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.28 % CPULimit : 300
% 0.12/0.28 % WCLimit : 300
% 0.12/0.28 % DateTime : Tue Sep 29 15:25:07 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.34 Running higher-order theorem proving
% 0.28/0.36 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.l3vryOKJWk/E---3.1_1424865.p
% 0.28/0.38 % Version: 3.5.1-ho
% 0.28/0.38 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.38 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.28/0.38 % Starting full_lambda_10 with 300s (1) cores
% 0.28/0.38 % Starting new_ho_8 with 300s (1) cores
% 0.28/0.38 % full_lambda_10 with pid 1424884 completed with status 0
% 0.28/0.38 % Result found by full_lambda_10
% 0.28/0.38 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.38 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.28/0.38 % Starting full_lambda_10 with 300s (1) cores
% 0.28/0.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.28/0.38 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.28/0.38 % Search class: HGHNS-FFSF11-SSSFFFNN
% 0.28/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.38 % SubtermCWHack with pid 1424886 completed with status 0
% 0.28/0.38 % Result found by SubtermCWHack
% 0.28/0.38 % Preprocessing class: HSSSSMSSSSSNSSA.
% 0.28/0.38 % Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.38 % Starting post_as_ho12 with 300s (1) cores
% 0.28/0.38 % Starting new_bool_9 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho4 with 300s (1) cores
% 0.28/0.38 % Starting post_as_ho2 with 300s (1) cores
% 0.28/0.38 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.28/0.38 % Starting full_lambda_10 with 300s (1) cores
% 0.28/0.38 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,5,,5,20000,3.0,true))
% 0.28/0.38 % SinE strategy is GSinE(CountFormulas,hypos,5,,5,20000,3.0,true)
% 0.28/0.38 % Search class: HGHNS-FFSF11-SSSFFFNN
% 0.28/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.38 % Preprocessing time : 0.001 s
% 0.28/0.38
% 0.28/0.38 % Proof found!
% 0.28/0.38 % SZS status Theorem
% 0.28/0.38 % SZS output start CNFRefutation
% See solution above
% 0.28/0.38 % Parsed axioms : 3
% 0.28/0.38 % Removed by relevancy pruning/SinE : 2
% 0.28/0.38 % Initial clauses : 10
% 0.28/0.38 % Removed in clause preprocessing : 0
% 0.28/0.38 % Initial clauses in saturation : 10
% 0.28/0.38 % Processed clauses : 51
% 0.28/0.38 % ...of these trivial : 0
% 0.28/0.38 % ...subsumed : 6
% 0.28/0.38 % ...remaining for further processing : 45
% 0.28/0.38 % Other redundant clauses eliminated : 0
% 0.28/0.38 % Clauses deleted for lack of memory : 0
% 0.28/0.38 % Backward-subsumed : 8
% 0.28/0.38 % Backward-rewritten : 14
% 0.28/0.38 % Generated clauses : 72
% 0.28/0.38 % ...of the previous two non-redundant : 72
% 0.28/0.38 % ...aggressively subsumed : 0
% 0.28/0.38 % Contextual simplify-reflections : 2
% 0.28/0.38 % Paramodulations : 72
% 0.28/0.38 % Factorizations : 0
% 0.28/0.38 % NegExts : 0
% 0.28/0.38 % Equation resolutions : 0
% 0.28/0.38 % Disequality decompositions : 0
% 0.28/0.38 % Total rewrite steps : 17
% 0.28/0.38 % ...of those cached : 13
% 0.28/0.38 % Propositional unsat checks : 0
% 0.28/0.38 % Propositional check models : 0
% 0.28/0.38 % Propositional check unsatisfiable : 0
% 0.28/0.38 % Propositional clauses : 0
% 0.28/0.38 % Propositional clauses after purity: 0
% 0.28/0.38 % Propositional unsat core size : 0
% 0.28/0.38 % Propositional preprocessing time : 0.000
% 0.28/0.38 % Propositional encoding time : 0.000
% 0.28/0.38 % Propositional solver time : 0.000
% 0.28/0.38 % Success case prop preproc time : 0.000
% 0.28/0.38 % Success case prop encoding time : 0.000
% 0.28/0.38 % Success case prop solver time : 0.000
% 0.28/0.38 % Current number of processed clauses : 23
% 0.28/0.38 % Positive orientable unit clauses : 5
% 0.28/0.38 % Positive unorientable unit clauses: 0
% 0.28/0.38 % Negative unit clauses : 1
% 0.28/0.38 % Non-unit-clauses : 17
% 0.28/0.38 % Current number of unprocessed clauses: 25
% 0.28/0.38 % ...number of literals in the above : 81
% 0.28/0.38 % Current number of archived formulas : 0
% 0.28/0.38 % Current number of archived clauses : 22
% 0.28/0.38 % Clause-clause subsumption calls (NU) : 223
% 0.28/0.38 % Rec. Clause-clause subsumption calls : 206
% 0.28/0.39 % Non-unit clause-clause subsumptions : 8
% 0.28/0.39 % Unit Clause-clause subsumption calls : 12
% 0.28/0.39 % Rewrite failures with RHS unbound : 0
% 0.28/0.39 % BW rewrite match attempts : 9
% 0.28/0.39 % BW rewrite match successes : 2
% 0.28/0.39 % Condensation attempts : 0
% 0.28/0.39 % Condensation successes : 0
% 0.28/0.39 % Termbank termtop insertions : 1832
% 0.28/0.39 % Search garbage collected termcells : 317
% 0.28/0.39
% 0.28/0.39 % -------------------------------------------------
% 0.28/0.39 % User time : 0.004 s
% 0.28/0.39 % System time : 0.003 s
% 0.28/0.39 % Total time : 0.007 s
% 0.28/0.39 % Maximum resident set size: 3888 pages
% 0.28/0.39
% 0.28/0.39 % -------------------------------------------------
% 0.28/0.39 % User time : 0.005 s
% 0.28/0.39 % System time : 0.008 s
% 0.28/0.39 % Total time : 0.013 s
% 0.28/0.39 % Maximum resident set size: 4864 pages
% 0.28/0.39 % E exiting
%------------------------------------------------------------------------------