%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU769^2 : 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 : n005.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 08:25:33 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 142 ( 7 ~; 3 |; 2 &; 119 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 45 ( 21 ^; 24 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
powerset: $i > $i ).
thf(decl_25,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_26,type,
dsetconstrER: $o ).
thf(decl_27,type,
subset: $i > $i > $o ).
thf(decl_28,type,
cartprod: $i > $i > $i ).
thf(decl_29,type,
breln: $i > $i > $i > $o ).
thf(decl_30,type,
breln1: $i > $i > $o ).
thf(decl_31,type,
breln1Set: $i > $i ).
thf(decl_32,type,
esk1_0: $i ).
thf(decl_33,type,
esk2_0: $i ).
thf(breln1,axiom,
( breln1
= ( ^ [X1: $i,X7: $i] : ( breln @ X1 @ X1 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDmFFTeZQi/E---3.1_1739737.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X5: $i,X6: $i] : ( subset @ X6 @ ( cartprod @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDmFFTeZQi/E---3.1_1739737.p',breln) ).
thf(breln1SetBreln1,conjecture,
( dsetconstrER
=> ! [X1: $i,X7: $i] :
( ( in @ X7 @ ( breln1Set @ X1 ) )
=> ( breln1 @ X1 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDmFFTeZQi/E---3.1_1739737.p',breln1SetBreln1) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDmFFTeZQi/E---3.1_1739737.p',dsetconstrER) ).
thf(breln1Set,axiom,
( breln1Set
= ( ^ [X1: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [X7: $i] : ( breln1 @ X1 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDmFFTeZQi/E---3.1_1739737.p',breln1Set) ).
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,
~ ( dsetconstrER
=> ! [X1: $i,X7: $i] :
( ( in @ X7 @ ( breln1Set @ X1 ) )
=> ( breln1 @ X1 @ X7 ) ) ),
inference(assume_negation,[status(cth)],[breln1SetBreln1]) ).
thf(c_0_8,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_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,
~ ( ! [X13: $i,X14: $i > $o,X15: $i] :
( ( in @ X15 @ ( dsetconstr @ X13 @ X14 ) )
=> ( X14 @ X15 ) )
=> ! [X1: $i,X7: $i] :
( ( in @ X7 @ ( breln1Set @ X1 ) )
=> ( subset @ X7 @ ( cartprod @ X1 @ X1 ) ) ) ),
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,
( breln1Set
= ( ^ [Z0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Z0 @ Z0 ) )
@ ^ [Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1Set]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X16: $i,X17: $i > $o,X18: $i] :
( ( ~ ( in @ X18 @ ( dsetconstr @ X16 @ X17 ) )
| ( X17 @ X18 ) )
& ( in @ esk2_0 @ ( breln1Set @ esk1_0 ) )
& ~ ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_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,
( breln1Set
= ( ^ [Z0: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ Z0 @ Z0 ) )
@ ^ [Z1: $i] : ( subset @ Z1 @ ( cartprod @ Z0 @ Z0 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
! [X1: $i] :
( ( dsetconstr @ ( powerset @ ( cartprod @ X1 @ X1 ) )
@ ^ [Z0: $i] : ( subset @ Z0 @ ( cartprod @ X1 @ X1 ) ) )
= ( breln1Set @ X1 ) ),
inference(arg_cong,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
~ ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i] :
( ( subset @ X1 @ ( cartprod @ X3 @ X3 ) )
| ~ ( in @ X1 @ ( breln1Set @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_18,negated_conjecture,
in @ esk2_0 @ ( breln1Set @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU769^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n005.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:23:31 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.21/0.27 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.kDmFFTeZQi/E---3.1_1739737.p
% 0.21/0.29 % Version: 3.5.1-ho
% 0.21/0.29 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.29 % Starting sh4l with 300s (1) cores
% 0.21/0.29 % Starting lpo8_s with 300s (1) cores
% 0.21/0.29 % ho_unfolding_6 with pid 1739751 completed with status 0
% 0.21/0.29 % Result found by ho_unfolding_6
% 0.21/0.29 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HHUSF-FFSF21-MSFFMSBN
% 0.21/0.29 % partial match(2): HHUSF-FFSF22-SSFFMSBN
% 0.21/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.29 % SubtermCWHack with pid 1739754 completed with status 0
% 0.21/0.29 % Result found by SubtermCWHack
% 0.21/0.29 % Preprocessing class: HSSSSMSSSLMNSFA.
% 0.21/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.29 % Starting new_ho_10 with 1500s (5) cores
% 0.21/0.29 % Starting ho_unfolding_6 with 300s (1) cores
% 0.21/0.29 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.21/0.29 % No SInE strategy applied
% 0.21/0.29 % Search class: HHUSF-FFSF21-MSFFMSBN
% 0.21/0.29 % partial match(2): HHUSF-FFSF22-SSFFMSBN
% 0.21/0.29 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.29 % Starting SubtermCWHack with 31s (1) cores
% 0.21/0.29 % Preprocessing time : 0.001 s
% 0.21/0.29
% 0.21/0.29 % Proof found!
% 0.21/0.29 % SZS status Theorem
% 0.21/0.29 % SZS output start CNFRefutation
% See solution above
% 0.21/0.29 % Parsed axioms : 14
% 0.21/0.29 % Removed by relevancy pruning/SinE : 0
% 0.21/0.29 % Initial clauses : 13
% 0.21/0.29 % Removed in clause preprocessing : 9
% 0.21/0.29 % Initial clauses in saturation : 4
% 0.21/0.29 % Processed clauses : 6
% 0.21/0.29 % ...of these trivial : 0
% 0.21/0.29 % ...subsumed : 0
% 0.21/0.29 % ...remaining for further processing : 6
% 0.21/0.29 % Other redundant clauses eliminated : 0
% 0.21/0.29 % Clauses deleted for lack of memory : 0
% 0.21/0.29 % Backward-subsumed : 0
% 0.21/0.29 % Backward-rewritten : 0
% 0.21/0.29 % Generated clauses : 3
% 0.21/0.29 % ...of the previous two non-redundant : 2
% 0.21/0.29 % ...aggressively subsumed : 0
% 0.21/0.29 % Contextual simplify-reflections : 0
% 0.21/0.29 % Paramodulations : 2
% 0.21/0.29 % Factorizations : 0
% 0.21/0.29 % NegExts : 0
% 0.21/0.29 % Equation resolutions : 0
% 0.21/0.29 % Disequality decompositions : 0
% 0.21/0.29 % Total rewrite steps : 1
% 0.21/0.29 % ...of those cached : 0
% 0.21/0.29 % Propositional unsat checks : 0
% 0.21/0.29 % Propositional check models : 0
% 0.21/0.29 % Propositional check unsatisfiable : 0
% 0.21/0.29 % Propositional clauses : 0
% 0.21/0.29 % Propositional clauses after purity: 0
% 0.21/0.29 % Propositional unsat core size : 0
% 0.21/0.29 % Propositional preprocessing time : 0.000
% 0.21/0.29 % Propositional encoding time : 0.000
% 0.21/0.29 % Propositional solver time : 0.000
% 0.21/0.29 % Success case prop preproc time : 0.000
% 0.21/0.29 % Success case prop encoding time : 0.000
% 0.21/0.29 % Success case prop solver time : 0.000
% 0.21/0.29 % Current number of processed clauses : 6
% 0.21/0.29 % Positive orientable unit clauses : 3
% 0.21/0.29 % Positive unorientable unit clauses: 0
% 0.21/0.29 % Negative unit clauses : 1
% 0.21/0.29 % Non-unit-clauses : 2
% 0.21/0.29 % Current number of unprocessed clauses: 0
% 0.21/0.29 % ...number of literals in the above : 0
% 0.21/0.29 % Current number of archived formulas : 0
% 0.21/0.29 % Current number of archived clauses : 0
% 0.21/0.29 % Clause-clause subsumption calls (NU) : 0
% 0.21/0.29 % Rec. Clause-clause subsumption calls : 0
% 0.21/0.29 % Non-unit clause-clause subsumptions : 0
% 0.21/0.29 % Unit Clause-clause subsumption calls : 0
% 0.21/0.29 % Rewrite failures with RHS unbound : 0
% 0.21/0.29 % BW rewrite match attempts : 0
% 0.21/0.29 % BW rewrite match successes : 0
% 0.21/0.29 % Condensation attempts : 0
% 0.21/0.29 % Condensation successes : 0
% 0.21/0.29 % Termbank termtop insertions : 651
% 0.21/0.29 % Search garbage collected termcells : 153
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.003 s
% 0.21/0.29 % System time : 0.003 s
% 0.21/0.29 % Total time : 0.006 s
% 0.21/0.29 % Maximum resident set size: 3640 pages
% 0.21/0.29
% 0.21/0.29 % -------------------------------------------------
% 0.21/0.29 % User time : 0.005 s
% 0.21/0.29 % System time : 0.008 s
% 0.21/0.29 % Total time : 0.012 s
% 0.21/0.29 % Maximum resident set size: 4608 pages
% 0.21/0.29 % E exiting
%------------------------------------------------------------------------------