%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU706^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:25:17 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 46 equ; 0 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 181 ( 17 ~; 12 |; 12 &; 100 @)
% ( 7 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 2 ^; 49 !; 3 ?; 54 :)
% 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,
uniqinunit: $o ).
thf(decl_28,type,
in__Cong: $o ).
thf(decl_29,type,
setadjoin__Cong: $o ).
thf(decl_30,type,
setunion__Cong: $o ).
thf(decl_31,type,
setunionsingleton: $o ).
thf(decl_32,type,
singleton: $i > $o ).
thf(decl_33,type,
esk1_0: $i ).
thf(decl_34,type,
esk2_0: $i ).
thf(decl_35,type,
esk3_0: $i ).
thf(theeq,conjecture,
( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X7: $i] :
( ( singleton @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X7 )
=> ( ( setunion @ X7 )
= X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',theeq) ).
thf(singleton,axiom,
( singleton
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X3
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',singleton) ).
thf(in__Cong,axiom,
( in__Cong
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( in @ X1 @ X3 )
<=> ( in @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',in__Cong) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',uniqinunit) ).
thf(setunionsingleton,axiom,
( setunionsingleton
<=> ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',setunionsingleton) ).
thf(setunion__Cong,axiom,
( setunion__Cong
<=> ! [X3: $i,X4: $i] :
( ( X3 = X4 )
=> ( ( setunion @ X3 )
= ( setunion @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',setunion__Cong) ).
thf(setadjoin__Cong,axiom,
( setadjoin__Cong
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ! [X5: $i,X6: $i] :
( ( X5 = X6 )
=> ( ( setadjoin @ X1 @ X5 )
= ( setadjoin @ X2 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.XUIIPDzhWZ/E---3.1_2724310.p',setadjoin__Cong) ).
thf(c_0_7,negated_conjecture,
~ ( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X7: $i] :
( ( singleton @ X7 )
=> ! [X1: $i] :
( ( in @ X1 @ X7 )
=> ( ( setunion @ X7 )
= X1 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[theeq]) ).
thf(c_0_8,plain,
( singleton
= ( ^ [Z0: $i] :
? [X1: $i] :
( ( in @ X1 @ Z0 )
& ( Z0
= ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(fof_simplification,[status(thm)],[singleton]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X23: $i,X24: $i] :
( ( in @ X23 @ ( setadjoin @ X24 @ emptyset ) )
=> ( X23 = X24 ) )
=> ( ! [X25: $i,X26: $i] :
( ( X25 = X26 )
=> ! [X27: $i,X28: $i] :
( ( X27 = X28 )
=> ( ( in @ X27 @ X25 )
<=> ( in @ X28 @ X26 ) ) ) )
=> ( ! [X29: $i,X30: $i] :
( ( X29 = X30 )
=> ! [X31: $i,X32: $i] :
( ( X31 = X32 )
=> ( ( setadjoin @ X29 @ X31 )
= ( setadjoin @ X30 @ X32 ) ) ) )
=> ( ! [X33: $i,X34: $i] :
( ( X33 = X34 )
=> ( ( setunion @ X33 )
= ( setunion @ X34 ) ) )
=> ( ! [X35: $i] :
( ( setunion @ ( setadjoin @ X35 @ emptyset ) )
= X35 )
=> ! [X7: $i] :
( ? [X36: $i] :
( ( in @ X36 @ X7 )
& ( X7
= ( setadjoin @ X36 @ emptyset ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X7 )
=> ( ( setunion @ X7 )
= X1 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,in__Cong]),c_0_8]),uniqinunit]),setunionsingleton]),setunion__Cong]),setadjoin__Cong]) ).
thf(c_0_10,negated_conjecture,
! [X37: $i,X38: $i,X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i] :
( ( ~ ( in @ X37 @ ( setadjoin @ X38 @ emptyset ) )
| ( X37 = X38 ) )
& ( ~ ( in @ X41 @ X39 )
| ( in @ X42 @ X40 )
| ( X41 != X42 )
| ( X39 != X40 ) )
& ( ~ ( in @ X42 @ X40 )
| ( in @ X41 @ X39 )
| ( X41 != X42 )
| ( X39 != X40 ) )
& ( ( X43 != X44 )
| ( X45 != X46 )
| ( ( setadjoin @ X43 @ X45 )
= ( setadjoin @ X44 @ X46 ) ) )
& ( ( X47 != X48 )
| ( ( setunion @ X47 )
= ( setunion @ X48 ) ) )
& ( ( setunion @ ( setadjoin @ X49 @ emptyset ) )
= X49 )
& ( in @ esk2_0 @ esk1_0 )
& ( esk1_0
= ( setadjoin @ esk2_0 @ emptyset ) )
& ( in @ esk3_0 @ esk1_0 )
& ( ( setunion @ esk1_0 )
!= 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(fof_nnf,[status(thm)],[c_0_9])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
( esk1_0
= ( setadjoin @ esk2_0 @ emptyset ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
( ( setunion @ esk1_0 )
!= esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
( ( setunion @ esk1_0 )
= esk2_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( X1 = esk2_0 )
| ~ ( in @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_17,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,negated_conjecture,
esk3_0 != esk2_0,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU706^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:12:44 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.XUIIPDzhWZ/E---3.1_2724310.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.08/0.26 % lpo1_def_fix with pid 2724325 completed with status 0
% 0.08/0.26 % Result found by lpo1_def_fix
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.08/0.26 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.08/0.26 % Search class: HHUSF-FFSS21-SSFFMFNN
% 0.08/0.26 % partial match(1): HHUSF-FFSF21-SSFFMFNN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 2724327 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.26 % Starting lpo1_def_fix with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.08/0.26 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.08/0.26 % Search class: HHUSF-FFSS21-SSFFMFNN
% 0.08/0.26 % partial match(1): HHUSF-FFSF21-SSFFMFNN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 17
% 0.08/0.26 % Removed by relevancy pruning/SinE : 10
% 0.08/0.26 % Initial clauses : 10
% 0.08/0.26 % Removed in clause preprocessing : 4
% 0.08/0.26 % Initial clauses in saturation : 6
% 0.08/0.26 % Processed clauses : 9
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 0
% 0.08/0.26 % ...remaining for further processing : 9
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 1
% 0.08/0.26 % Generated clauses : 3
% 0.08/0.26 % ...of the previous two non-redundant : 3
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 3
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 1
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 8
% 0.08/0.26 % Positive orientable unit clauses : 5
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 1
% 0.08/0.26 % Non-unit-clauses : 2
% 0.08/0.26 % Current number of unprocessed clauses: 0
% 0.08/0.26 % ...number of literals in the above : 0
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 1
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 1
% 0.08/0.26 % BW rewrite match successes : 1
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 1099
% 0.08/0.26 % Search garbage collected termcells : 438
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.004 s
% 0.08/0.26 % System time : 0.001 s
% 0.08/0.26 % Total time : 0.004 s
% 0.08/0.26 % Maximum resident set size: 3640 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.007 s
% 0.08/0.26 % System time : 0.003 s
% 0.08/0.26 % Total time : 0.010 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------