%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU787^2 : TPTP v9.3.1. Released v3.7.0.
% 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 08:25:38 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 0 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 308 ( 24 ~; 21 |; 8 &; 214 @)
% ( 1 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
binunion: $i > $i > $i ).
thf(decl_25,type,
kpair: $i > $i > $i ).
thf(decl_26,type,
breln1: $i > $i > $o ).
thf(decl_27,type,
breln1unionE: $o ).
thf(decl_28,type,
esk1_0: $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(decl_31,type,
esk4_0: $i ).
thf(decl_32,type,
esk5_0: $i ).
thf(decl_33,type,
epred1_0: $o ).
thf(breln1unionEcases,conjecture,
( breln1unionE
=> ! [X1: $i,X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X2 @ X3 ) )
=> ! [X6: $o] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> X6 )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> X6 )
=> X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.omLYjG5Gpz/E---3.1_1365218.p',breln1unionEcases) ).
thf(breln1unionE,axiom,
( breln1unionE
<=> ! [X1: $i,X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X2 @ X3 ) )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
| ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.omLYjG5Gpz/E---3.1_1365218.p',breln1unionE) ).
thf(c_0_2,negated_conjecture,
~ ( breln1unionE
=> ! [X1: $i,X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X2 @ X3 ) )
=> ! [X6: $o] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> X6 )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> X6 )
=> X6 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1unionEcases]) ).
thf(c_0_3,negated_conjecture,
~ ( ! [X18: $i,X19: $i] :
( ( breln1 @ X18 @ X19 )
=> ! [X20: $i] :
( ( breln1 @ X18 @ X20 )
=> ! [X21: $i] :
( ( in @ X21 @ X18 )
=> ! [X22: $i] :
( ( in @ X22 @ X18 )
=> ( ( in @ ( kpair @ X21 @ X22 ) @ ( binunion @ X19 @ X20 ) )
=> ( ( in @ ( kpair @ X21 @ X22 ) @ X19 )
| ( in @ ( kpair @ X21 @ X22 ) @ X20 ) ) ) ) ) ) )
=> ! [X1: $i,X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln1 @ X1 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X2 @ X3 ) )
=> ! [X6: $o] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> X6 )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> X6 )
=> X6 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_2,breln1unionE]) ).
thf(c_0_4,negated_conjecture,
! [X23: $i,X24: $i,X25: $i,X26: $i,X27: $i] :
( ( ~ ( breln1 @ X23 @ X24 )
| ~ ( breln1 @ X23 @ X25 )
| ~ ( in @ X26 @ X23 )
| ~ ( in @ X27 @ X23 )
| ~ ( in @ ( kpair @ X26 @ X27 ) @ ( binunion @ X24 @ X25 ) )
| ( in @ ( kpair @ X26 @ X27 ) @ X24 )
| ( in @ ( kpair @ X26 @ X27 ) @ X25 ) )
& ( breln1 @ esk1_0 @ esk2_0 )
& ( breln1 @ esk1_0 @ esk3_0 )
& ( in @ esk4_0 @ esk1_0 )
& ( in @ esk5_0 @ esk1_0 )
& ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( binunion @ esk2_0 @ esk3_0 ) )
& ( ~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ esk2_0 )
| epred1_0 )
& ( ~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ esk3_0 )
| epred1_0 )
& ~ epred1_0 ),
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_3])])])])]) ).
thf(c_0_5,negated_conjecture,
( epred1_0
| ~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,negated_conjecture,
( epred1_0
| ~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i,X5: $i,X4: $i,X3: $i] :
( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
| ( in @ ( kpair @ X4 @ X5 ) @ X3 )
| ~ ( breln1 @ X1 @ X2 )
| ~ ( breln1 @ X1 @ X3 )
| ~ ( in @ X4 @ X1 )
| ~ ( in @ X5 @ X1 )
| ~ ( in @ ( kpair @ X4 @ X5 ) @ ( binunion @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_9,negated_conjecture,
in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( binunion @ esk2_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_10,negated_conjecture,
~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ esk2_0 ),
inference(sr,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_11,negated_conjecture,
~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ esk3_0 ),
inference(sr,[status(thm)],[c_0_7,c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ~ ( in @ esk5_0 @ X1 )
| ~ ( in @ esk4_0 @ X1 )
| ~ ( breln1 @ X1 @ esk3_0 )
| ~ ( breln1 @ X1 @ esk2_0 ) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
breln1 @ esk1_0 @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_14,negated_conjecture,
in @ esk5_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_15,negated_conjecture,
in @ esk4_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_16,negated_conjecture,
breln1 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU787^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:29:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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.omLYjG5Gpz/E---3.1_1365218.p
% 0.07/0.26 % Version: 3.5.1-ho
% 0.07/0.26 % Preprocessing class: HSSSSMSSSLSNFFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.07/0.26 % sh5l with pid 1365232 completed with status 0
% 0.07/0.26 % Result found by sh5l
% 0.07/0.26 % Preprocessing class: HSSSSMSSSLSNFFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGUNF-FFSS22-SFFFMFNN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % SubtermCWHack with pid 1365235 completed with status 0
% 0.07/0.26 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSSSSMSSSLSNFFN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.26 % Starting sh5l with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGUNF-FFSS22-SFFFMFNN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 7
% 0.07/0.26 % Removed by relevancy pruning/SinE : 5
% 0.07/0.26 % Initial clauses : 9
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 9
% 0.07/0.26 % Processed clauses : 10
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 10
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 2
% 0.07/0.26 % ...of the previous two non-redundant : 1
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 2
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 3
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 10
% 0.07/0.26 % Positive orientable unit clauses : 5
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 3
% 0.07/0.26 % Non-unit-clauses : 2
% 0.07/0.26 % Current number of unprocessed clauses: 0
% 0.07/0.26 % ...number of literals in the above : 0
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 0
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 1
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 0
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 1056
% 0.07/0.26 % Search garbage collected termcells : 344
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.005 s
% 0.07/0.26 % System time : 0.000 s
% 0.07/0.26 % Total time : 0.005 s
% 0.07/0.26 % Maximum resident set size: 3636 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.006 s
% 0.07/0.26 % System time : 0.004 s
% 0.07/0.26 % Total time : 0.010 s
% 0.07/0.26 % Maximum resident set size: 4864 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------