%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU776^2 : 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 : 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 08:25:35 AM UTC 2026
% Result : Theorem 0.11s 0.24s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 267 ( 13 ~; 9 |; 5 &; 214 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 73 ( 30 ^; 43 !; 0 ?; 73 :)
% 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,
breln1invset: $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(breln1,axiom,
( breln1
= ( ^ [X1: $i,X9: $i] : ( breln @ X1 @ X1 @ X9 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IGVBAgW63Z/E---3.1_800756.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IGVBAgW63Z/E---3.1_800756.p',breln) ).
thf(breln1invI,conjecture,
( dpsetconstrI
=> ! [X1: $i,X9: $i] :
( ( breln1 @ X1 @ X9 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X9 )
=> ( in @ ( kpair @ X6 @ X5 ) @ ( breln1invset @ X1 @ X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IGVBAgW63Z/E---3.1_800756.p',breln1invI) ).
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/sandbox2/tmp/tmp.IGVBAgW63Z/E---3.1_800756.p',dpsetconstrI) ).
thf(breln1invset,axiom,
( breln1invset
= ( ^ [X1: $i,X9: $i] :
( dpsetconstr @ X1 @ X1
@ ^ [X5: $i,X6: $i] : ( in @ ( kpair @ X6 @ X5 ) @ X9 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.IGVBAgW63Z/E---3.1_800756.p',breln1invset) ).
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 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X9 )
=> ( in @ ( kpair @ X6 @ X5 ) @ ( breln1invset @ X1 @ X9 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1invI]) ).
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,
~ ( ! [X19: $i,X20: $i,X21: $i > $i > $o,X22: $i] :
( ( in @ X22 @ X19 )
=> ! [X23: $i] :
( ( in @ X23 @ X20 )
=> ( ( X21 @ X22 @ X23 )
=> ( in @ ( kpair @ X22 @ X23 ) @ ( dpsetconstr @ X19 @ X20 @ X21 ) ) ) ) )
=> ! [X1: $i,X9: $i] :
( ( subset @ X9 @ ( cartprod @ X1 @ X1 ) )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X9 )
=> ( in @ ( kpair @ X6 @ X5 ) @ ( breln1invset @ X1 @ X9 ) ) ) ) ) ) ),
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,
( breln1invset
= ( ^ [Z0: $i,Z1: $i] :
( dpsetconstr @ Z0 @ Z0
@ ^ [Z2: $i,Z3: $i] : ( in @ ( kpair @ Z3 @ Z2 ) @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1invset]) ).
thf(c_0_12,negated_conjecture,
! [X24: $i,X25: $i,X26: $i > $i > $o,X27: $i,X28: $i] :
( ( ~ ( in @ X27 @ X24 )
| ~ ( in @ X28 @ X25 )
| ~ ( X26 @ X27 @ X28 )
| ( in @ ( kpair @ X27 @ X28 ) @ ( dpsetconstr @ X24 @ X25 @ X26 ) ) )
& ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ( in @ esk3_0 @ esk1_0 )
& ( in @ esk4_0 @ esk1_0 )
& ( in @ ( kpair @ esk3_0 @ esk4_0 ) @ esk2_0 )
& ~ ( in @ ( kpair @ esk4_0 @ esk3_0 ) @ ( breln1invset @ esk1_0 @ esk2_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,
( breln1invset
= ( ^ [Z0: $i,Z1: $i] :
( dpsetconstr @ Z0 @ Z0
@ ^ [Z2: $i,Z3: $i] : ( in @ ( kpair @ Z3 @ Z2 ) @ Z1 ) ) ) ),
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] :
( ( dpsetconstr @ X1 @ X1
@ ^ [Z0: $i,Z1: $i] : ( in @ ( kpair @ Z1 @ Z0 ) @ X2 ) )
= ( breln1invset @ X1 @ X2 ) ),
inference(arg_cong,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
~ ( in @ ( kpair @ esk4_0 @ esk3_0 ) @ ( breln1invset @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X2: $i,X5: $i,X3: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ ( breln1invset @ X3 @ X5 ) )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ X5 )
| ~ ( in @ X2 @ X3 )
| ~ ( in @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
in @ ( kpair @ esk3_0 @ esk4_0 ) @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_20,negated_conjecture,
in @ esk4_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU776^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n006.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Tue Sep 29 14:27:40 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running higher-order theorem proving
% 0.11/0.22 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.IGVBAgW63Z/E---3.1_800756.p
% 0.11/0.24 % Version: 3.5.1-ho
% 0.11/0.24 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.11/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.11/0.24 % Starting sh4l with 300s (1) cores
% 0.11/0.24 % Starting lpo8_s with 300s (1) cores
% 0.11/0.24 % ho_unfolding_6 with pid 800787 completed with status 0
% 0.11/0.24 % Result found by ho_unfolding_6
% 0.11/0.24 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.11/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.11/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.24 % No SInE strategy applied
% 0.11/0.24 % Search class: HHUSF-FFSS32-DSFFMSBN
% 0.11/0.24 % partial match(1): HHUSF-FFSS32-SSFFMSBN
% 0.11/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.24 % SubtermCWHack with pid 800790 completed with status 0
% 0.11/0.24 % Result found by SubtermCWHack
% 0.11/0.24 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.11/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.11/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.11/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.24 % No SInE strategy applied
% 0.11/0.24 % Search class: HHUSF-FFSS32-DSFFMSBN
% 0.11/0.24 % partial match(1): HHUSF-FFSS32-SSFFMSBN
% 0.11/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.24 % Preprocessing time : 0.001 s
% 0.11/0.24
% 0.11/0.24 % Proof found!
% 0.11/0.24 % SZS status Theorem
% 0.11/0.24 % SZS output start CNFRefutation
% See solution above
% 0.11/0.24 % Parsed axioms : 14
% 0.11/0.24 % Removed by relevancy pruning/SinE : 0
% 0.11/0.24 % Initial clauses : 16
% 0.11/0.24 % Removed in clause preprocessing : 9
% 0.11/0.24 % Initial clauses in saturation : 7
% 0.11/0.24 % Processed clauses : 11
% 0.11/0.24 % ...of these trivial : 1
% 0.11/0.24 % ...subsumed : 0
% 0.11/0.24 % ...remaining for further processing : 10
% 0.11/0.24 % Other redundant clauses eliminated : 0
% 0.11/0.24 % Clauses deleted for lack of memory : 0
% 0.11/0.24 % Backward-subsumed : 0
% 0.11/0.24 % Backward-rewritten : 0
% 0.11/0.24 % Generated clauses : 5
% 0.11/0.24 % ...of the previous two non-redundant : 4
% 0.11/0.24 % ...aggressively subsumed : 0
% 0.11/0.24 % Contextual simplify-reflections : 0
% 0.11/0.24 % Paramodulations : 2
% 0.11/0.24 % Factorizations : 0
% 0.11/0.24 % NegExts : 0
% 0.11/0.24 % Equation resolutions : 0
% 0.11/0.24 % Disequality decompositions : 0
% 0.11/0.24 % Total rewrite steps : 4
% 0.11/0.24 % ...of those cached : 0
% 0.11/0.24 % Propositional unsat checks : 0
% 0.11/0.24 % Propositional check models : 0
% 0.11/0.24 % Propositional check unsatisfiable : 0
% 0.11/0.24 % Propositional clauses : 0
% 0.11/0.24 % Propositional clauses after purity: 0
% 0.11/0.24 % Propositional unsat core size : 0
% 0.11/0.24 % Propositional preprocessing time : 0.000
% 0.11/0.24 % Propositional encoding time : 0.000
% 0.11/0.24 % Propositional solver time : 0.000
% 0.11/0.24 % Success case prop preproc time : 0.000
% 0.11/0.24 % Success case prop encoding time : 0.000
% 0.11/0.24 % Success case prop solver time : 0.000
% 0.11/0.24 % Current number of processed clauses : 10
% 0.11/0.24 % Positive orientable unit clauses : 7
% 0.11/0.24 % Positive unorientable unit clauses: 0
% 0.11/0.24 % Negative unit clauses : 1
% 0.11/0.24 % Non-unit-clauses : 2
% 0.11/0.24 % Current number of unprocessed clauses: 0
% 0.11/0.24 % ...number of literals in the above : 0
% 0.11/0.24 % Current number of archived formulas : 0
% 0.11/0.24 % Current number of archived clauses : 0
% 0.11/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.24 % Non-unit clause-clause subsumptions : 0
% 0.11/0.24 % Unit Clause-clause subsumption calls : 0
% 0.11/0.24 % Rewrite failures with RHS unbound : 0
% 0.11/0.24 % BW rewrite match attempts : 1
% 0.11/0.24 % BW rewrite match successes : 0
% 0.11/0.24 % Condensation attempts : 0
% 0.11/0.24 % Condensation successes : 0
% 0.11/0.24 % Termbank termtop insertions : 1025
% 0.11/0.24 % Search garbage collected termcells : 269
% 0.11/0.24
% 0.11/0.24 % -------------------------------------------------
% 0.11/0.24 % User time : 0.004 s
% 0.11/0.24 % System time : 0.001 s
% 0.11/0.24 % Total time : 0.005 s
% 0.11/0.24 % Maximum resident set size: 3900 pages
% 0.11/0.24
% 0.11/0.24 % -------------------------------------------------
% 0.11/0.24 % User time : 0.005 s
% 0.11/0.24 % System time : 0.006 s
% 0.11/0.24 % Total time : 0.011 s
% 0.11/0.24 % Maximum resident set size: 4864 pages
% 0.11/0.24 % E exiting
%------------------------------------------------------------------------------