%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU619^2 : 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 : n008.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 08:26:57 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 360 ( 10 ~; 5 |; 8 &; 329 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 2 ^; 27 !; 6 ?; 35 :)
% 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,
iskpair: $i > $o ).
thf(decl_28,type,
setukpairIL: $o ).
thf(decl_29,type,
setukpairIR: $o ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(kpairiskpair,conjecture,
( setukpairIL
=> ( setukpairIR
=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vAfZQdlkaq/E---3.1_3199782.p',kpairiskpair) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ X1 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ X1 ) )
& ( X1
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vAfZQdlkaq/E---3.1_3199782.p',iskpair) ).
thf(setukpairIR,axiom,
( setukpairIR
<=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vAfZQdlkaq/E---3.1_3199782.p',setukpairIR) ).
thf(setukpairIL,axiom,
( setukpairIL
<=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.vAfZQdlkaq/E---3.1_3199782.p',setukpairIL) ).
thf(c_0_4,negated_conjecture,
~ ( setukpairIL
=> ( setukpairIR
=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(assume_negation,[status(cth)],[kpairiskpair]) ).
thf(c_0_5,plain,
( iskpair
= ( ^ [Z0: $i] :
? [X2: $i] :
( ( in @ X2 @ ( setunion @ Z0 ) )
& ? [X3: $i] :
( ( in @ X3 @ ( setunion @ Z0 ) )
& ( Z0
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iskpair]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X10: $i,X11: $i] : ( in @ X10 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [X12: $i,X13: $i] : ( in @ X13 @ ( setunion @ ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X13 @ emptyset ) ) @ emptyset ) ) ) )
=> ! [X2: $i,X3: $i] :
? [X14: $i] :
( ( in @ X14 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X15: $i] :
( ( in @ X15 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X15 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,setukpairIR]),setukpairIL]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X16: $i,X17: $i,X18: $i,X19: $i,X22: $i,X23: $i] :
( ( in @ X16 @ ( setunion @ ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X17 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ X19 @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
& ( ~ ( in @ X22 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X23 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X23 @ emptyset ) ) @ 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] :
( ~ ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X2: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU619^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n008.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:59:24 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.vAfZQdlkaq/E---3.1_3199782.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.24 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.24 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.09/0.24 % lpo1_def_fix with pid 3199821 completed with status 0
% 0.09/0.24 % Result found by lpo1_def_fix
% 0.09/0.24 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.24 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.09/0.24 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.09/0.24 % Search class: HUHSS-FFSF21-MSFFMFNN
% 0.09/0.24 % partial match(2): HHUSS-FFSF21-MSFFMFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 3199823 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSSSSLSSSLSNSFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.24 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf600_gu_R05_F100_L20000)
% 0.09/0.24 % SinE strategy is gf600_gu_R05_F100_L20000
% 0.09/0.24 % Search class: HUHSS-FFSF21-MSFFMFNN
% 0.09/0.24 % partial match(2): HHUSS-FFSF21-MSFFMFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 11
% 0.09/0.24 % Removed by relevancy pruning/SinE : 7
% 0.09/0.24 % Initial clauses : 3
% 0.09/0.24 % Removed in clause preprocessing : 0
% 0.09/0.24 % Initial clauses in saturation : 3
% 0.09/0.24 % Processed clauses : 4
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 4
% 0.09/0.24 % Other redundant clauses eliminated : 0
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 0
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 4
% 0.09/0.24 % ...of the previous two non-redundant : 3
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 4
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 0
% 0.09/0.24 % Equation resolutions : 0
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 0
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 4
% 0.09/0.24 % Positive orientable unit clauses : 2
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 0
% 0.09/0.24 % Non-unit-clauses : 2
% 0.09/0.24 % Current number of unprocessed clauses: 1
% 0.09/0.24 % ...number of literals in the above : 2
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 0
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 1
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 0
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 1
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 977
% 0.09/0.24 % Search garbage collected termcells : 161
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.000 s
% 0.09/0.24 % System time : 0.004 s
% 0.09/0.24 % Total time : 0.004 s
% 0.09/0.24 % Maximum resident set size: 3632 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.000 s
% 0.09/0.24 % System time : 0.010 s
% 0.09/0.24 % Total time : 0.010 s
% 0.09/0.24 % Maximum resident set size: 4864 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------