%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU584^2 : 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 : 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 08:24:36 AM UTC 2026
% Result : Theorem 0.07s 0.13s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 142 ( 9 ~; 5 |; 3 &; 110 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 4 ^; 32 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
thf(decl_26,type,
setunion: $i > $i ).
thf(decl_27,type,
setunionI: $o ).
thf(decl_28,type,
binunion: $i > $i > $i ).
thf(decl_29,type,
upairset2IR: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(binunionIR,conjecture,
( setunionI
=> ( upairset2IR
=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binunion @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IWUBpcHQVQ/E---3.1_140155.p',binunionIR) ).
thf(binunion,axiom,
( binunion
= ( ^ [X2: $i,X4: $i] : ( setunion @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IWUBpcHQVQ/E---3.1_140155.p',binunion) ).
thf(upairset2IR,axiom,
( upairset2IR
<=> ! [X2: $i,X4: $i] : ( in @ X4 @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IWUBpcHQVQ/E---3.1_140155.p',upairset2IR) ).
thf(setunionI,axiom,
( setunionI
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IWUBpcHQVQ/E---3.1_140155.p',setunionI) ).
thf(c_0_4,negated_conjecture,
~ ( setunionI
=> ( upairset2IR
=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binunion @ X1 @ X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[binunionIR]) ).
thf(c_0_5,plain,
( binunion
= ( ^ [Z0: $i,Z1: $i] : ( setunion @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[binunion]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X13: $i,X14: $i,X15: $i] :
( ( in @ X14 @ X15 )
=> ( ( in @ X15 @ X13 )
=> ( in @ X14 @ ( setunion @ X13 ) ) ) )
=> ( ! [X16: $i,X17: $i] : ( in @ X17 @ ( setadjoin @ X16 @ ( setadjoin @ X17 @ emptyset ) ) )
=> ! [X1: $i,X3: $i,X2: $i] :
( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),upairset2IR]),setunionI]) ).
thf(c_0_7,negated_conjecture,
! [X18: $i,X19: $i,X20: $i,X21: $i,X22: $i] :
( ( ~ ( in @ X19 @ X20 )
| ~ ( in @ X20 @ X18 )
| ( in @ X19 @ ( setunion @ X18 ) ) )
& ( in @ X22 @ ( setadjoin @ X21 @ ( setadjoin @ X22 @ emptyset ) ) )
& ( in @ esk3_0 @ esk2_0 )
& ~ ( in @ esk3_0 @ ( setunion @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) ) ) ),
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_6])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( in @ esk3_0 @ ( setunion @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
in @ esk3_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU584^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Sep 29 13:52:03 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 Running higher-order theorem proving
% 0.07/0.12 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.IWUBpcHQVQ/E---3.1_140155.p
% 0.07/0.13 % Version: 3.5.1-ho
% 0.07/0.13 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.13 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.13 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.13 % Starting lpo1_def_fix with 300s (1) cores
% 0.07/0.13 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.07/0.13 % ehoh_best_sine_rwall with pid 140169 completed with status 0
% 0.07/0.13 % Result found by ehoh_best_sine_rwall
% 0.07/0.13 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.13 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.13 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.13 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.13 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.13 % Search class: HHUNF-FFSF21-MSFFMFNN
% 0.07/0.13 % partial match(1): HHUNF-FFSF21-MFFFMFNN
% 0.07/0.13 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.13 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.13 % SubtermCWHack with pid 140172 completed with status 0
% 0.07/0.13 % Result found by SubtermCWHack
% 0.07/0.13 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.07/0.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.13 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.13 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.13 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.13 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.13 % Search class: HHUNF-FFSF21-MSFFMFNN
% 0.07/0.13 % partial match(1): HHUNF-FFSF21-MFFFMFNN
% 0.07/0.13 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.13 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.13 % Preprocessing time : 0.001 s
% 0.07/0.13
% 0.07/0.13 % Proof found!
% 0.07/0.13 % SZS status Theorem
% 0.07/0.13 % SZS output start CNFRefutation
% See solution above
% 0.07/0.13 % Parsed axioms : 11
% 0.07/0.13 % Removed by relevancy pruning/SinE : 7
% 0.07/0.13 % Initial clauses : 4
% 0.07/0.13 % Removed in clause preprocessing : 0
% 0.07/0.13 % Initial clauses in saturation : 4
% 0.07/0.13 % Processed clauses : 6
% 0.07/0.13 % ...of these trivial : 0
% 0.07/0.13 % ...subsumed : 0
% 0.07/0.13 % ...remaining for further processing : 6
% 0.07/0.13 % Other redundant clauses eliminated : 0
% 0.07/0.13 % Clauses deleted for lack of memory : 0
% 0.07/0.13 % Backward-subsumed : 0
% 0.07/0.13 % Backward-rewritten : 0
% 0.07/0.13 % Generated clauses : 5
% 0.07/0.13 % ...of the previous two non-redundant : 3
% 0.07/0.13 % ...aggressively subsumed : 0
% 0.07/0.13 % Contextual simplify-reflections : 0
% 0.07/0.13 % Paramodulations : 5
% 0.07/0.13 % Factorizations : 0
% 0.07/0.13 % NegExts : 0
% 0.07/0.13 % Equation resolutions : 0
% 0.07/0.13 % Disequality decompositions : 0
% 0.07/0.13 % Total rewrite steps : 1
% 0.07/0.13 % ...of those cached : 0
% 0.07/0.13 % Propositional unsat checks : 0
% 0.07/0.13 % Propositional check models : 0
% 0.07/0.13 % Propositional check unsatisfiable : 0
% 0.07/0.13 % Propositional clauses : 0
% 0.07/0.13 % Propositional clauses after purity: 0
% 0.07/0.13 % Propositional unsat core size : 0
% 0.07/0.13 % Propositional preprocessing time : 0.000
% 0.07/0.13 % Propositional encoding time : 0.000
% 0.07/0.13 % Propositional solver time : 0.000
% 0.07/0.13 % Success case prop preproc time : 0.000
% 0.07/0.13 % Success case prop encoding time : 0.000
% 0.07/0.13 % Success case prop solver time : 0.000
% 0.07/0.13 % Current number of processed clauses : 6
% 0.07/0.13 % Positive orientable unit clauses : 2
% 0.07/0.13 % Positive unorientable unit clauses: 0
% 0.07/0.13 % Negative unit clauses : 1
% 0.07/0.13 % Non-unit-clauses : 3
% 0.07/0.13 % Current number of unprocessed clauses: 1
% 0.07/0.13 % ...number of literals in the above : 3
% 0.07/0.13 % Current number of archived formulas : 0
% 0.07/0.13 % Current number of archived clauses : 0
% 0.07/0.13 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.13 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.13 % Non-unit clause-clause subsumptions : 0
% 0.07/0.13 % Unit Clause-clause subsumption calls : 0
% 0.07/0.13 % Rewrite failures with RHS unbound : 0
% 0.07/0.13 % BW rewrite match attempts : 0
% 0.07/0.13 % BW rewrite match successes : 0
% 0.07/0.13 % Condensation attempts : 0
% 0.07/0.13 % Condensation successes : 0
% 0.07/0.13 % Termbank termtop insertions : 587
% 0.07/0.13 % Search garbage collected termcells : 165
% 0.07/0.13
% 0.07/0.13 % -------------------------------------------------
% 0.07/0.13 % User time : 0.003 s
% 0.07/0.13 % System time : 0.000 s
% 0.07/0.13 % Total time : 0.003 s
% 0.07/0.13 % Maximum resident set size: 3632 pages
% 0.07/0.13
% 0.07/0.13 % -------------------------------------------------
% 0.07/0.13 % User time : 0.003 s
% 0.07/0.13 % System time : 0.003 s
% 0.07/0.13 % Total time : 0.006 s
% 0.07/0.13 % Maximum resident set size: 4608 pages
% 0.07/0.13 % E exiting
%------------------------------------------------------------------------------