%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU780^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 0.27s 0.27s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 9 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 406 ( 15 ~; 10 |; 22 &; 336 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-5 aty)
% Number of variables : 106 ( 33 ^; 65 !; 8 ?; 106 :)
% 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,
dpsetconstrER: $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_5: $i > $i > $i > $i > $i > $i ).
thf(breln1,axiom,
( breln1
= ( ^ [X1: $i,X9: $i] : ( breln @ X1 @ X1 @ X9 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t15A9BsOb6/E---3.1_3440070.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t15A9BsOb6/E---3.1_3440070.p',breln) ).
thf(breln1compE,conjecture,
( dpsetconstrER
=> ! [X1: $i,X9: $i] :
( ( breln1 @ X1 @ X9 )
=> ! [X10: $i] :
( ( breln1 @ X1 @ X10 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) )
=> ? [X7: $i] :
( ( in @ X7 @ X1 )
& ( in @ ( kpair @ X5 @ X7 ) @ X9 )
& ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t15A9BsOb6/E---3.1_3440070.p',breln1compE) ).
thf(dpsetconstrER,axiom,
( dpsetconstrER
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i,X6: $i] :
( ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [X7: $i,X8: $i] : ( X4 @ X7 @ X8 ) ) )
=> ( X4 @ X5 @ X6 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.t15A9BsOb6/E---3.1_3440070.p',dpsetconstrER) ).
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/sandbox2/tmp/tmp.t15A9BsOb6/E---3.1_3440070.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,
~ ( dpsetconstrER
=> ! [X1: $i,X9: $i] :
( ( breln1 @ X1 @ X9 )
=> ! [X10: $i] :
( ( breln1 @ X1 @ X10 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) )
=> ? [X7: $i] :
( ( in @ X7 @ X1 )
& ( in @ ( kpair @ X5 @ X7 ) @ X9 )
& ( in @ ( kpair @ X7 @ X6 ) @ X10 ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1compE]) ).
thf(c_0_8,plain,
( dpsetconstrER
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o,X5: $i,X6: $i] :
( ( in @ ( kpair @ X5 @ X6 )
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i,Z1: $i] : ( X4 @ Z0 @ Z1 ) ) )
=> ( X4 @ X5 @ X6 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).
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,X26: $i] :
( ( in @ ( kpair @ X25 @ X26 ) @ ( dpsetconstr @ X22 @ X23 @ X24 ) )
=> ( X24 @ X25 @ X26 ) )
=> ! [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 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ ( breln1compset @ X1 @ X9 @ X10 ) )
=> ? [X7: $i] :
( ( in @ X7 @ X1 )
& ( in @ ( kpair @ X5 @ X7 ) @ X9 )
& ( in @ ( kpair @ X7 @ X6 ) @ 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,X37: $i] :
( ( ~ ( in @ ( kpair @ X30 @ X31 ) @ ( dpsetconstr @ X27 @ X28 @ X29 ) )
| ( X29 @ X30 @ X31 ) )
& ( 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 @ ( kpair @ esk4_0 @ esk5_0 ) @ ( breln1compset @ esk1_0 @ esk2_0 @ esk3_0 ) )
& ( ~ ( in @ X37 @ esk1_0 )
| ~ ( in @ ( kpair @ esk4_0 @ X37 ) @ esk2_0 )
| ~ ( in @ ( kpair @ X37 @ esk5_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,
! [X1: $i,X2: $i,X3: $i,X5: $i,X4: $i > $i > $o] :
( ( X4 @ X1 @ X2 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ ( dpsetconstr @ X3 @ X5 @ X4 ) ) ),
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,X3: $i,X5: $i,X6: $i] :
( ? [X53: $i] :
( ( in @ X53 @ X1 )
& ( in @ ( kpair @ X2 @ X53 ) @ X3 )
& ( in @ ( kpair @ X53 @ X5 ) @ X6 ) )
| ~ ( in @ ( kpair @ X2 @ X5 ) @ ( breln1compset @ X1 @ X3 @ X6 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X6: $i] :
( ( in @ ( kpair @ ( esk6_5 @ X1 @ X2 @ X3 @ X5 @ X6 ) @ X5 ) @ X6 )
| ~ ( in @ ( kpair @ X2 @ X5 ) @ ( breln1compset @ X1 @ X3 @ X6 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_16]) ).
thf(c_0_18,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_19,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X6: $i] :
( ( in @ ( esk6_5 @ X1 @ X2 @ X3 @ X5 @ X6 ) @ X1 )
| ~ ( in @ ( kpair @ X2 @ X5 ) @ ( breln1compset @ X1 @ X3 @ X6 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_16]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i] :
( ~ ( in @ X1 @ esk1_0 )
| ~ ( in @ ( kpair @ esk4_0 @ X1 ) @ esk2_0 )
| ~ ( in @ ( kpair @ X1 @ esk5_0 ) @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_21,negated_conjecture,
in @ ( kpair @ ( esk6_5 @ esk1_0 @ esk4_0 @ esk2_0 @ esk5_0 @ esk3_0 ) @ esk5_0 ) @ esk3_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_22,negated_conjecture,
in @ ( esk6_5 @ esk1_0 @ esk4_0 @ esk2_0 @ esk5_0 @ esk3_0 ) @ esk1_0,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X5: $i,X6: $i] :
( ( in @ ( kpair @ X1 @ ( esk6_5 @ X2 @ X1 @ X3 @ X5 @ X6 ) ) @ X3 )
| ~ ( in @ ( kpair @ X1 @ X5 ) @ ( breln1compset @ X2 @ X3 @ X6 ) ) ),
inference(dynamic_cnf,[status(thm)],[c_0_16]) ).
thf(c_0_24,negated_conjecture,
~ ( in @ ( kpair @ esk4_0 @ ( esk6_5 @ esk1_0 @ esk4_0 @ esk2_0 @ esk5_0 @ esk3_0 ) ) @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
thf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU780^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.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 14:26:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.t15A9BsOb6/E---3.1_3440070.p
% 0.27/0.27 % Version: 3.5.1-ho
% 0.27/0.27 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.27/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.27/0.27 % Starting sh4l with 300s (1) cores
% 0.27/0.27 % Starting lpo8_s with 300s (1) cores
% 0.27/0.27 % sh4l with pid 3440103 completed with status 0
% 0.27/0.27 % Result found by sh4l
% 0.27/0.27 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.27/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.27/0.27 % Starting sh4l with 300s (1) cores
% 0.27/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.27 % No SInE strategy applied
% 0.27/0.27 % Search class: HHHSF-FFSM32-DSFFMSBN
% 0.27/0.27 % partial match(3): HHUSF-FFSS32-SSFFMSBN
% 0.27/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.27 % SubtermCWHack with pid 3440105 completed with status 0
% 0.27/0.27 % Result found by SubtermCWHack
% 0.27/0.27 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.27/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.27 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.27 % Starting ho_unfolding_6 with 300s (1) cores
% 0.27/0.27 % Starting sh4l with 300s (1) cores
% 0.27/0.27 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.27/0.27 % No SInE strategy applied
% 0.27/0.27 % Search class: HHHSF-FFSM32-DSFFMSBN
% 0.27/0.27 % partial match(3): HHUSF-FFSS32-SSFFMSBN
% 0.27/0.27 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.27 % Starting SubtermCWHack with 31s (1) cores
% 0.27/0.27 % Preprocessing time : 0.001 s
% 0.27/0.27
% 0.27/0.27 % Proof found!
% 0.27/0.27 % SZS status Theorem
% 0.27/0.27 % SZS output start CNFRefutation
% See solution above
% 0.27/0.27 % Parsed axioms : 14
% 0.27/0.27 % Removed by relevancy pruning/SinE : 0
% 0.27/0.27 % Initial clauses : 17
% 0.27/0.27 % Removed in clause preprocessing : 9
% 0.27/0.27 % Initial clauses in saturation : 8
% 0.27/0.27 % Processed clauses : 21
% 0.27/0.27 % ...of these trivial : 3
% 0.27/0.27 % ...subsumed : 0
% 0.27/0.27 % ...remaining for further processing : 18
% 0.27/0.27 % Other redundant clauses eliminated : 0
% 0.27/0.27 % Clauses deleted for lack of memory : 0
% 0.27/0.27 % Backward-subsumed : 0
% 0.27/0.27 % Backward-rewritten : 0
% 0.27/0.27 % Generated clauses : 14
% 0.27/0.27 % ...of the previous two non-redundant : 13
% 0.27/0.27 % ...aggressively subsumed : 0
% 0.27/0.27 % Contextual simplify-reflections : 0
% 0.27/0.27 % Paramodulations : 5
% 0.27/0.27 % Factorizations : 0
% 0.27/0.27 % NegExts : 0
% 0.27/0.27 % Equation resolutions : 0
% 0.27/0.27 % Disequality decompositions : 0
% 0.27/0.27 % Total rewrite steps : 4
% 0.27/0.27 % ...of those cached : 0
% 0.27/0.27 % Propositional unsat checks : 0
% 0.27/0.27 % Propositional check models : 0
% 0.27/0.27 % Propositional check unsatisfiable : 0
% 0.27/0.27 % Propositional clauses : 0
% 0.27/0.27 % Propositional clauses after purity: 0
% 0.27/0.27 % Propositional unsat core size : 0
% 0.27/0.27 % Propositional preprocessing time : 0.000
% 0.27/0.27 % Propositional encoding time : 0.000
% 0.27/0.27 % Propositional solver time : 0.000
% 0.27/0.27 % Success case prop preproc time : 0.000
% 0.27/0.27 % Success case prop encoding time : 0.000
% 0.27/0.27 % Success case prop solver time : 0.000
% 0.27/0.27 % Current number of processed clauses : 17
% 0.27/0.27 % Positive orientable unit clauses : 11
% 0.27/0.27 % Positive unorientable unit clauses: 0
% 0.27/0.27 % Negative unit clauses : 1
% 0.27/0.27 % Non-unit-clauses : 5
% 0.27/0.27 % Current number of unprocessed clauses: 0
% 0.27/0.27 % ...number of literals in the above : 0
% 0.27/0.27 % Current number of archived formulas : 0
% 0.27/0.27 % Current number of archived clauses : 1
% 0.27/0.27 % Clause-clause subsumption calls (NU) : 11
% 0.27/0.27 % Rec. Clause-clause subsumption calls : 11
% 0.27/0.27 % Non-unit clause-clause subsumptions : 0
% 0.27/0.27 % Unit Clause-clause subsumption calls : 1
% 0.27/0.27 % Rewrite failures with RHS unbound : 0
% 0.27/0.27 % BW rewrite match attempts : 4
% 0.27/0.27 % BW rewrite match successes : 0
% 0.27/0.27 % Condensation attempts : 0
% 0.27/0.27 % Condensation successes : 0
% 0.27/0.27 % Termbank termtop insertions : 1654
% 0.27/0.27 % Search garbage collected termcells : 324
% 0.27/0.27
% 0.27/0.27 % -------------------------------------------------
% 0.27/0.27 % User time : 0.004 s
% 0.27/0.27 % System time : 0.003 s
% 0.27/0.27 % Total time : 0.007 s
% 0.27/0.27 % Maximum resident set size: 3644 pages
% 0.27/0.27
% 0.27/0.27 % -------------------------------------------------
% 0.27/0.27 % User time : 0.006 s
% 0.27/0.27 % System time : 0.006 s
% 0.27/0.27 % Total time : 0.013 s
% 0.27/0.27 % Maximum resident set size: 4864 pages
% 0.27/0.27 % E exiting
%------------------------------------------------------------------------------