%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU620^2 : 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 : n019.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 08:24:45 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 20 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 458 ( 14 ~; 7 |; 13 &; 420 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 53 ( 4 ^; 39 !; 10 ?; 53 :)
% 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,
kpairiskpair: $o ).
thf(decl_29,type,
kpair: $i > $i > $i ).
thf(decl_30,type,
esk1_2: $i > $i > $i ).
thf(decl_31,type,
esk2_2: $i > $i > $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
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.x7t3onA3ux/E---3.1_812318.p',iskpair) ).
thf(kpairp,conjecture,
( kpairiskpair
=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x7t3onA3ux/E---3.1_812318.p',kpairp) ).
thf(kpairiskpair,axiom,
( kpairiskpair
<=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x7t3onA3ux/E---3.1_812318.p',kpairiskpair) ).
thf(kpair,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x7t3onA3ux/E---3.1_812318.p',kpair) ).
thf(c_0_4,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_5,negated_conjecture,
~ ( kpairiskpair
=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
inference(assume_negation,[status(cth)],[kpairp]) ).
thf(c_0_6,axiom,
( kpairiskpair
= ( ! [X2: $i,X3: $i] :
? [X8: $i] :
( ( in @ X8 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X9: $i] :
( ( in @ X9 @ ( 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 @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X9 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[kpairiskpair,c_0_4]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X10: $i,X11: $i] :
? [X12: $i] :
( ( in @ X12 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X13: $i] :
( ( in @ X13 @ ( setunion @ ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X10 @ ( setadjoin @ X11 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X12 @ ( setadjoin @ X13 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ! [X2: $i,X3: $i] :
? [X14: $i] :
( ( in @ X14 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
& ? [X15: $i] :
( ( in @ X15 @ ( setunion @ ( kpair @ X2 @ X3 ) ) )
& ( ( kpair @ X2 @ X3 )
= ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X15 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_4]) ).
thf(c_0_8,plain,
! [X16: $i,X17: $i] :
( ( kpair @ X16 @ X17 )
= ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X17 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_9,negated_conjecture,
! [X18: $i,X19: $i,X24: $i,X25: $i] :
( ( in @ ( esk1_2 @ X18 @ X19 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( esk2_2 @ X18 @ X19 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X19 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X18 @ X19 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X18 @ X19 ) @ ( setadjoin @ ( esk2_2 @ X18 @ X19 ) @ emptyset ) ) @ emptyset ) ) )
& ( ~ ( in @ X24 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ~ ( in @ X25 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ( ( kpair @ esk3_0 @ esk4_0 )
!= ( setadjoin @ ( setadjoin @ X24 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X24 @ ( setadjoin @ X25 @ 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_7])])])])]) ).
thf(c_0_10,plain,
! [X26: $i,X27: $i] :
( ( kpair @ X26 @ X27 )
= ( setadjoin @ ( setadjoin @ X26 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X26 @ ( setadjoin @ X27 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ( ( kpair @ esk3_0 @ esk4_0 )
!= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk2_2 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i,X1: $i] :
( ( ( kpair @ esk3_0 @ esk4_0 )
!= ( kpair @ X1 @ X2 ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) ) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk2_2 @ X1 @ X2 ) @ ( setunion @ ( kpair @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk1_2 @ X1 @ X2 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( ( kpair @ X1 @ ( esk2_2 @ esk3_0 @ esk4_0 ) )
!= ( kpair @ esk3_0 @ esk4_0 ) )
| ~ ( in @ X1 @ ( setunion @ ( kpair @ esk3_0 @ esk4_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i] : ( in @ ( esk1_2 @ X1 @ X2 ) @ ( setunion @ ( kpair @ X1 @ X2 ) ) ),
inference(rw,[status(thm)],[c_0_16,c_0_12]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X2: $i] :
( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X2 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_2 @ X1 @ X2 ) @ ( setadjoin @ ( esk2_2 @ X1 @ X2 ) @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_20,negated_conjecture,
( ( kpair @ ( esk1_2 @ esk3_0 @ esk4_0 ) @ ( esk2_2 @ esk3_0 @ esk4_0 ) )
!= ( kpair @ esk3_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i] :
( ( kpair @ ( esk1_2 @ X1 @ X2 ) @ ( esk2_2 @ X1 @ X2 ) )
= ( kpair @ X1 @ X2 ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12]),c_0_12]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU620^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:58:47 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.23 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.x7t3onA3ux/E---3.1_812318.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.25 % Starting sh4l with 300s (1) cores
% 0.09/0.25 % Starting ho_unfolding_2 with 300s (1) cores
% 0.09/0.25 % post_as_ho5 with pid 812332 completed with status 0
% 0.09/0.25 % Result found by post_as_ho5
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.09/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.09/0.25 % Search class: HUHSM-FFSF21-MSFFMFNN
% 0.09/0.25 % partial match(3): HGHSF-FFSF21-SSFFMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 812335 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.09/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.09/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.09/0.25 % Search class: HUHSM-FFSF21-MSFFMFNN
% 0.09/0.25 % partial match(3): HGHSF-FFSF21-SSFFMFNN
% 0.09/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.09/0.25 % Preprocessing time : 0.001 s
% 0.09/0.25
% 0.09/0.25 % Proof found!
% 0.09/0.25 % SZS status Theorem
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25 % Parsed axioms : 11
% 0.09/0.25 % Removed by relevancy pruning/SinE : 7
% 0.09/0.25 % Initial clauses : 5
% 0.09/0.25 % Removed in clause preprocessing : 0
% 0.09/0.25 % Initial clauses in saturation : 5
% 0.09/0.25 % Processed clauses : 11
% 0.09/0.25 % ...of these trivial : 0
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 11
% 0.09/0.25 % Other redundant clauses eliminated : 0
% 0.09/0.25 % Clauses deleted for lack of memory : 0
% 0.09/0.25 % Backward-subsumed : 0
% 0.09/0.25 % Backward-rewritten : 1
% 0.09/0.25 % Generated clauses : 11
% 0.09/0.25 % ...of the previous two non-redundant : 7
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 11
% 0.09/0.25 % Factorizations : 0
% 0.09/0.25 % NegExts : 0
% 0.09/0.25 % Equation resolutions : 0
% 0.09/0.25 % Disequality decompositions : 0
% 0.09/0.25 % Total rewrite steps : 8
% 0.09/0.25 % ...of those cached : 4
% 0.09/0.25 % Propositional unsat checks : 0
% 0.09/0.25 % Propositional check models : 0
% 0.09/0.25 % Propositional check unsatisfiable : 0
% 0.09/0.25 % Propositional clauses : 0
% 0.09/0.25 % Propositional clauses after purity: 0
% 0.09/0.25 % Propositional unsat core size : 0
% 0.09/0.25 % Propositional preprocessing time : 0.000
% 0.09/0.25 % Propositional encoding time : 0.000
% 0.09/0.25 % Propositional solver time : 0.000
% 0.09/0.25 % Success case prop preproc time : 0.000
% 0.09/0.25 % Success case prop encoding time : 0.000
% 0.09/0.25 % Success case prop solver time : 0.000
% 0.09/0.25 % Current number of processed clauses : 10
% 0.09/0.25 % Positive orientable unit clauses : 5
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 2
% 0.09/0.25 % Non-unit-clauses : 3
% 0.09/0.25 % Current number of unprocessed clauses: 1
% 0.09/0.25 % ...number of literals in the above : 1
% 0.09/0.25 % Current number of archived formulas : 0
% 0.09/0.25 % Current number of archived clauses : 1
% 0.09/0.25 % Clause-clause subsumption calls (NU) : 4
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 2
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 10
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 1
% 0.09/0.25 % BW rewrite match successes : 1
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 1113
% 0.09/0.25 % Search garbage collected termcells : 178
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.004 s
% 0.09/0.25 % System time : 0.001 s
% 0.09/0.25 % Total time : 0.005 s
% 0.09/0.25 % Maximum resident set size: 3632 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.005 s
% 0.09/0.25 % System time : 0.006 s
% 0.09/0.25 % Total time : 0.011 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------