%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU631^2 : 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 : n006.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 08:24:48 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 15 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 249 ( 17 ~; 12 |; 18 &; 191 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 12 ^; 44 !; 16 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_26,type,
powerset: $i > $i ).
thf(decl_27,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_28,type,
dsetconstrER: $o ).
thf(decl_29,type,
binunion: $i > $i > $i ).
thf(decl_30,type,
kpair: $i > $i > $i ).
thf(decl_31,type,
cartprod: $i > $i > $i ).
thf(decl_32,type,
esk1_0: $i ).
thf(decl_33,type,
esk2_0: $i ).
thf(decl_34,type,
esk3_0: $i ).
thf(decl_35,type,
esk4_3: $i > $i > $i > $i ).
thf(decl_36,type,
esk5_3: $i > $i > $i > $i ).
thf(cartprodmempair1,conjecture,
( dsetconstrER
=> ! [X1: $i,X5: $i,X7: $i] :
( ( in @ X7 @ ( cartprod @ X1 @ X5 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X4: $i] :
( ( in @ X4 @ X5 )
& ( X7
= ( kpair @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4rQXylHQXk/E---3.1_760730.p',cartprodmempair1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4rQXylHQXk/E---3.1_760730.p',dsetconstrER) ).
thf(cartprod,axiom,
( cartprod
= ( ^ [X1: $i,X5: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ X5 ) ) )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X1 )
& ? [X6: $i] :
( ( in @ X6 @ X5 )
& ( X3
= ( kpair @ X4 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4rQXylHQXk/E---3.1_760730.p',cartprod) ).
thf(c_0_3,negated_conjecture,
~ ( dsetconstrER
=> ! [X1: $i,X5: $i,X7: $i] :
( ( in @ X7 @ ( cartprod @ X1 @ X5 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X4: $i] :
( ( in @ X4 @ X5 )
& ( X7
= ( kpair @ X3 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodmempair1]) ).
thf(c_0_4,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X16: $i,X17: $i > $o,X18: $i] :
( ( in @ X18 @ ( dsetconstr @ X16 @ X17 ) )
=> ( X17 @ X18 ) )
=> ! [X1: $i,X5: $i,X7: $i] :
( ( in @ X7 @ ( cartprod @ X1 @ X5 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X4: $i] :
( ( in @ X4 @ X5 )
& ( X7
= ( kpair @ X3 @ X4 ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,c_0_4])]) ).
thf(c_0_6,plain,
( cartprod
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Z0 @ Z1 ) ) )
@ ^ [Z2: $i] :
? [X4: $i] :
( ( in @ X4 @ Z0 )
& ? [X6: $i] :
( ( in @ X6 @ Z1 )
& ( Z2
= ( kpair @ X4 @ X6 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cartprod]) ).
thf(c_0_7,negated_conjecture,
! [X19: $i,X20: $i > $o,X21: $i,X25: $i,X26: $i] :
( ( ~ ( in @ X21 @ ( dsetconstr @ X19 @ X20 ) )
| ( X20 @ X21 ) )
& ( in @ esk3_0 @ ( cartprod @ esk1_0 @ esk2_0 ) )
& ( ~ ( in @ X25 @ esk1_0 )
| ~ ( in @ X26 @ esk2_0 )
| ( esk3_0
!= ( kpair @ X25 @ X26 ) ) ) ),
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_5])])])])]) ).
thf(c_0_8,plain,
( cartprod
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Z0 @ Z1 ) ) )
@ ^ [Z2: $i] :
? [X40: $i] :
( ( in @ X40 @ Z0 )
& ? [X41: $i] :
( ( in @ X41 @ Z1 )
& ( Z2
= ( kpair @ X40 @ X41 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,plain,
! [X1: $i,X3: $i] :
( ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X1 @ X3 ) ) )
@ ^ [Z0: $i] :
? [X42: $i] :
( ( in @ X42 @ X1 )
& ? [X43: $i] :
( ( in @ X43 @ X3 )
& ( Z0
= ( kpair @ X42 @ X43 ) ) ) ) )
= ( cartprod @ X1 @ X3 ) ),
inference(arg_cong,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ? [X44: $i] :
( ( in @ X44 @ X1 )
& ? [X45: $i] :
( ( in @ X45 @ X3 )
& ( X4
= ( kpair @ X44 @ X45 ) ) ) )
| ~ ( in @ X4 @ ( cartprod @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( in @ X1 @ esk1_0 )
| ~ ( in @ X3 @ esk2_0 )
| ( esk3_0
!= ( kpair @ X1 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( ( kpair @ ( esk4_3 @ X1 @ X3 @ X4 ) @ ( esk5_3 @ X1 @ X3 @ X4 ) )
= X3 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X4 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ ( esk5_3 @ X1 @ X3 @ X4 ) @ X4 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X4 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
in @ esk3_0 @ ( cartprod @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ ( esk4_3 @ X1 @ X3 @ X4 ) @ X1 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X4 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_11]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( in @ ( esk5_3 @ X1 @ esk3_0 @ X3 ) @ esk2_0 )
| ~ ( in @ ( esk4_3 @ X1 @ esk3_0 @ X3 ) @ esk1_0 )
| ~ ( in @ esk3_0 @ ( cartprod @ X1 @ X3 ) ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13])]) ).
thf(c_0_18,negated_conjecture,
in @ ( esk5_3 @ esk1_0 @ esk3_0 @ esk2_0 ) @ esk2_0,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
in @ ( esk4_3 @ esk1_0 @ esk3_0 @ esk2_0 ) @ esk1_0,
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU631^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n006.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:00:01 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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.4rQXylHQXk/E---3.1_760730.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % partial match(1): HSSSSMSSSLMNSFA
% 0.07/0.25 % Preprocessing class: HSSSSMSSSMMNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % Starting sh4l with 300s (1) cores
% 0.07/0.25 % Starting lpo8_s with 300s (1) cores
% 0.07/0.25 % ho_unfolding_6 with pid 760744 completed with status 0
% 0.07/0.25 % Result found by ho_unfolding_6
% 0.07/0.25 % partial match(1): HSSSSMSSSLMNSFA
% 0.07/0.25 % Preprocessing class: HSSSSMSSSMMNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHSF-FFSS21-DSFFSSBN
% 0.07/0.25 % partial match(5): HGHSF-FFSF22-SSFFMSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 760747 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.25 % partial match(1): HSSSSMSSSLMNSFA
% 0.07/0.25 % Preprocessing class: HSSSSMSSSMMNSFA.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.07/0.25 % No SInE strategy applied
% 0.07/0.25 % Search class: HHHSF-FFSS21-DSFFSSBN
% 0.07/0.25 % partial match(5): HGHSF-FFSF22-SSFFMSBN
% 0.07/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.25 % Preprocessing time : 0.001 s
% 0.07/0.25
% 0.07/0.25 % Proof found!
% 0.07/0.25 % SZS status Theorem
% 0.07/0.25 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25 % Parsed axioms : 13
% 0.07/0.25 % Removed by relevancy pruning/SinE : 0
% 0.07/0.25 % Initial clauses : 14
% 0.07/0.25 % Removed in clause preprocessing : 9
% 0.07/0.25 % Initial clauses in saturation : 5
% 0.07/0.25 % Processed clauses : 18
% 0.07/0.25 % ...of these trivial : 1
% 0.07/0.25 % ...subsumed : 0
% 0.07/0.25 % ...remaining for further processing : 17
% 0.07/0.25 % Other redundant clauses eliminated : 1
% 0.07/0.25 % Clauses deleted for lack of memory : 0
% 0.07/0.25 % Backward-subsumed : 0
% 0.07/0.25 % Backward-rewritten : 0
% 0.07/0.25 % Generated clauses : 18
% 0.07/0.25 % ...of the previous two non-redundant : 15
% 0.07/0.25 % ...aggressively subsumed : 0
% 0.07/0.25 % Contextual simplify-reflections : 0
% 0.07/0.25 % Paramodulations : 8
% 0.07/0.25 % Factorizations : 0
% 0.07/0.25 % NegExts : 0
% 0.07/0.25 % Equation resolutions : 1
% 0.07/0.25 % Disequality decompositions : 0
% 0.07/0.25 % Total rewrite steps : 5
% 0.07/0.25 % ...of those cached : 0
% 0.07/0.25 % Propositional unsat checks : 0
% 0.07/0.25 % Propositional check models : 0
% 0.07/0.25 % Propositional check unsatisfiable : 0
% 0.07/0.25 % Propositional clauses : 0
% 0.07/0.25 % Propositional clauses after purity: 0
% 0.07/0.25 % Propositional unsat core size : 0
% 0.07/0.25 % Propositional preprocessing time : 0.000
% 0.07/0.25 % Propositional encoding time : 0.000
% 0.07/0.25 % Propositional solver time : 0.000
% 0.07/0.25 % Success case prop preproc time : 0.000
% 0.07/0.25 % Success case prop encoding time : 0.000
% 0.07/0.25 % Success case prop solver time : 0.000
% 0.07/0.25 % Current number of processed clauses : 16
% 0.07/0.25 % Positive orientable unit clauses : 10
% 0.07/0.25 % Positive unorientable unit clauses: 0
% 0.07/0.25 % Negative unit clauses : 0
% 0.07/0.25 % Non-unit-clauses : 6
% 0.07/0.25 % Current number of unprocessed clauses: 2
% 0.07/0.25 % ...number of literals in the above : 3
% 0.07/0.25 % Current number of archived formulas : 0
% 0.07/0.25 % Current number of archived clauses : 1
% 0.07/0.25 % Clause-clause subsumption calls (NU) : 12
% 0.07/0.25 % Rec. Clause-clause subsumption calls : 11
% 0.07/0.25 % Non-unit clause-clause subsumptions : 0
% 0.07/0.25 % Unit Clause-clause subsumption calls : 0
% 0.07/0.25 % Rewrite failures with RHS unbound : 0
% 0.07/0.25 % BW rewrite match attempts : 2
% 0.07/0.25 % BW rewrite match successes : 0
% 0.07/0.25 % Condensation attempts : 0
% 0.07/0.25 % Condensation successes : 0
% 0.07/0.25 % Termbank termtop insertions : 1468
% 0.07/0.25 % Search garbage collected termcells : 206
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.004 s
% 0.07/0.25 % System time : 0.002 s
% 0.07/0.25 % Total time : 0.006 s
% 0.07/0.25 % Maximum resident set size: 3640 pages
% 0.07/0.25
% 0.07/0.25 % -------------------------------------------------
% 0.07/0.25 % User time : 0.005 s
% 0.07/0.25 % System time : 0.007 s
% 0.07/0.25 % Total time : 0.012 s
% 0.07/0.25 % Maximum resident set size: 4864 pages
% 0.07/0.25 % E exiting
%------------------------------------------------------------------------------