%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU779^2 : 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 : n026.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 08:25:36 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 9 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 424 ( 22 ~; 18 |; 18 &; 331 @)
% ( 2 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 98 ( 33 ^; 60 !; 5 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
kpair: $i > $i > $i ).
thf(decl_26,type,
cartprod: $i > $i > $i ).
thf(decl_27,type,
breln: $i > $i > $i > $o ).
thf(decl_28,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_29,type,
dpsetconstrI: $o ).
thf(decl_30,type,
breln1: $i > $i > $o ).
thf(decl_31,type,
breln1compset: $i > $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_0: $i ).
thf(decl_36,type,
esk5_0: $i ).
thf(decl_37,type,
esk6_0: $i ).
thf(breln1,axiom,
( breln1
= ( ^ [X1: $i,X9: $i] : ( breln @ X1 @ X1 @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sizxw7qqVE/E---3.1_674739.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sizxw7qqVE/E---3.1_674739.p',breln) ).
thf(breln1compI,conjecture,
( dpsetconstrI
=> ! [X1: $i,X9: $i] :
( ( breln1 @ X1 @ X9 )
=> ! [X10: $i] :
( ( breln1 @ X1 @ X10 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X9 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X10 )
=> ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sizxw7qqVE/E---3.1_674739.p',breln1compI) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X4 @ X5 @ X6 )
=> ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i,X8: $i] : ( X4 @ X7 @ X8 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sizxw7qqVE/E---3.1_674739.p',dpsetconstrI) ).
thf(breln1compset,axiom,
( breln1compset
= ( ^ [X1: $i,X9: $i,X10: $i] :
( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] :
? [X7: $i] :
( ( in @ X7 @ X1 )
& ( in @ ( kpair @ X5 @ X7 ) @ X9 )
& ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.sizxw7qqVE/E---3.1_674739.p',breln1compset) ).
thf(c_0_5,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1]) ).
thf(c_0_6,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_7,negated_conjecture,
~ ( dpsetconstrI
=> ! [X1: $i,X9: $i] :
( ( breln1 @ X1 @ X9 )
=> ! [X10: $i] :
( ( breln1 @ X1 @ X10 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X9 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X10 )
=> ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1compI]) ).
thf(c_0_8,plain,
( dpsetconstrI
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X4 @ X5 @ X6 )
=> ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i,Z1: $i] : ( X4 @ Z0 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).
thf(c_0_9,plain,
( breln1
= ( ^ [Z0: $i,Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i > $i > $o,X25: $i] :
( ( in @ X25 @ X22 )
=> ! [X26: $i] :
( ( in @ X26 @ X23 )
=> ( ( X24 @ X25 @ X26 )
=> ( in @ ( kpair @ X25 @ X26 ) @ ( dpsetconstr @ X22 @ X23 @ X24 ) ) ) ) )
=> ! [X1: $i,X9: $i] :
( ( subset @ X9 @ ( cartprod @ X1 @ X1 ) )
=> ! [X10: $i] :
( ( subset @ X10 @ ( cartprod @ X1 @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X7 ) @ X9 )
=> ( ( in @ ( kpair @ X7 @ X6 ) @ X10 )
=> ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) ) ) ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9])]) ).
thf(c_0_11,plain,
( breln1compset
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( dpsetconstr @ Z0 @ Z0
@ ^ [Z3: $i,Z4: $i] :
? [X7: $i] :
( ( in @ X7 @ Z0 )
& ( in @ ( kpair @ Z3 @ X7 ) @ Z1 )
& ( in @ ( kpair @ X7 @ Z4 ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1compset]) ).
thf(c_0_12,negated_conjecture,
! [X27: $i,X28: $i,X29: $i > $i > $o,X30: $i,X31: $i] :
( ( ~ ( in @ X30 @ X27 )
| ~ ( in @ X31 @ X28 )
| ~ ( X29 @ X30 @ X31 )
| ( in @ ( kpair @ X30 @ X31 ) @ ( dpsetconstr @ X27 @ X28 @ X29 ) ) )
& ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ( subset @ esk3_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ( in @ esk4_0 @ esk1_0 )
& ( in @ esk5_0 @ esk1_0 )
& ( in @ esk6_0 @ esk1_0 )
& ( in @ ( kpair @ esk4_0 @ esk6_0 ) @ esk2_0 )
& ( in @ ( kpair @ esk6_0 @ esk5_0 ) @ esk3_0 )
& ~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( breln1compset @ esk1_0 @ esk2_0 @ esk3_0 ) ) ),
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_10])])])])]) ).
thf(c_0_13,plain,
( breln1compset
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( dpsetconstr @ Z0 @ Z0
@ ^ [Z3: $i,Z4: $i] :
? [X51: $i] :
( ( in @ X51 @ Z0 )
& ( in @ ( kpair @ Z3 @ X51 ) @ Z1 )
& ( in @ ( kpair @ X51 @ Z4 ) @ Z2 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i,X1: $i,X5: $i,X4: $i > $i > $o,X3: $i] :
( ( in @ ( kpair @ X1 @ X3 ) @ ( dpsetconstr @ X2 @ X5 @ X4 ) )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X5 )
| ~ ( X4 @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( dpsetconstr @ X1 @ X1
@ ^ [Z0: $i,Z1: $i] :
? [X52: $i] :
( ( in @ X52 @ X1 )
& ( in @ ( kpair @ Z0 @ X52 ) @ X2 )
& ( in @ ( kpair @ X52 @ Z1 ) @ X3 ) ) )
= ( breln1compset @ X1 @ X2 @ X3 ) ),
inference(arg_cong,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X6: $i,X5: $i,X3: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X5 @ X6 ) )
| ~ ? [X53: $i] :
( ( in @ X53 @ X3 )
& ( in @ ( kpair @ X1 @ X53 ) @ X5 )
& ( in @ ( kpair @ X53 @ X2 ) @ X6 ) )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i,X5: $i,X7: $i,X6: $i,X3: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X5 @ X6 ) )
| ~ ( in @ ( kpair @ X1 @ X7 ) @ X5 )
| ~ ( in @ ( kpair @ X7 @ X2 ) @ X6 )
| ~ ( in @ X7 @ X3 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X1 @ X3 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_16]) ).
thf(c_0_18,negated_conjecture,
in @ ( kpair @ esk4_0 @ esk6_0 ) @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,negated_conjecture,
~ ( in @ ( kpair @ esk4_0 @ esk5_0 ) @ ( breln1compset @ esk1_0 @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ esk4_0 @ X1 ) @ ( breln1compset @ X2 @ esk2_0 @ X3 ) )
| ~ ( in @ ( kpair @ esk6_0 @ X1 ) @ X3 )
| ~ ( in @ esk6_0 @ X2 )
| ~ ( in @ esk4_0 @ X2 )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
in @ ( kpair @ esk6_0 @ esk5_0 ) @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,negated_conjecture,
in @ esk6_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_23,negated_conjecture,
in @ esk4_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_24,negated_conjecture,
in @ esk5_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU779^2 : 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 : n026.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 14:30:42 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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.sizxw7qqVE/E---3.1_674739.p
% 0.09/0.25 % Version: 3.5.1-ho
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.25 % Starting sh4l with 300s (1) cores
% 0.09/0.25 % Starting lpo8_s with 300s (1) cores
% 0.09/0.25 % sh4l with pid 674772 completed with status 0
% 0.09/0.25 % Result found by sh4l
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.25 % Starting sh4l with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HHUSF-FFSM32-DSFFMSBN
% 0.09/0.25 % partial match(2): HHUSF-FFSS32-SSFFMSBN
% 0.09/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.25 % SubtermCWHack with pid 674775 completed with status 0
% 0.09/0.25 % Result found by SubtermCWHack
% 0.09/0.25 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.09/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.25 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.25 % Starting ho_unfolding_6 with 300s (1) cores
% 0.09/0.25 % Starting sh4l with 300s (1) cores
% 0.09/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.25 % No SInE strategy applied
% 0.09/0.25 % Search class: HHUSF-FFSM32-DSFFMSBN
% 0.09/0.25 % partial match(2): HHUSF-FFSS32-SSFFMSBN
% 0.09/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.25 % Starting SubtermCWHack with 31s (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 : 14
% 0.09/0.25 % Removed by relevancy pruning/SinE : 0
% 0.09/0.25 % Initial clauses : 19
% 0.09/0.25 % Removed in clause preprocessing : 9
% 0.09/0.25 % Initial clauses in saturation : 10
% 0.09/0.25 % Processed clauses : 20
% 0.09/0.25 % ...of these trivial : 3
% 0.09/0.25 % ...subsumed : 0
% 0.09/0.25 % ...remaining for further processing : 17
% 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 : 0
% 0.09/0.25 % Generated clauses : 14
% 0.09/0.25 % ...of the previous two non-redundant : 13
% 0.09/0.25 % ...aggressively subsumed : 0
% 0.09/0.25 % Contextual simplify-reflections : 0
% 0.09/0.25 % Paramodulations : 7
% 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 : 7
% 0.09/0.25 % ...of those cached : 0
% 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 : 16
% 0.09/0.25 % Positive orientable unit clauses : 11
% 0.09/0.25 % Positive unorientable unit clauses: 0
% 0.09/0.25 % Negative unit clauses : 1
% 0.09/0.25 % Non-unit-clauses : 4
% 0.09/0.25 % Current number of unprocessed clauses: 2
% 0.09/0.25 % ...number of literals in the above : 17
% 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) : 0
% 0.09/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.25 % Non-unit clause-clause subsumptions : 0
% 0.09/0.25 % Unit Clause-clause subsumption calls : 0
% 0.09/0.25 % Rewrite failures with RHS unbound : 0
% 0.09/0.25 % BW rewrite match attempts : 4
% 0.09/0.25 % BW rewrite match successes : 0
% 0.09/0.25 % Condensation attempts : 0
% 0.09/0.25 % Condensation successes : 0
% 0.09/0.25 % Termbank termtop insertions : 1907
% 0.09/0.25 % Search garbage collected termcells : 359
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.002 s
% 0.09/0.25 % System time : 0.003 s
% 0.09/0.25 % Total time : 0.006 s
% 0.09/0.25 % Maximum resident set size: 3644 pages
% 0.09/0.25
% 0.09/0.25 % -------------------------------------------------
% 0.09/0.25 % User time : 0.004 s
% 0.09/0.25 % System time : 0.008 s
% 0.09/0.25 % Total time : 0.012 s
% 0.09/0.25 % Maximum resident set size: 4864 pages
% 0.09/0.25 % E exiting
%------------------------------------------------------------------------------