%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU666^2 : 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 : 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 08:24:57 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 7 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 221 ( 8 ~; 7 |; 18 &; 172 @)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 17 ^; 41 !; 10 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrEL: $o ).
thf(decl_26,type,
subset: $i > $i > $o ).
thf(decl_27,type,
subsetI2: $o ).
thf(decl_28,type,
kpair: $i > $i > $i ).
thf(decl_29,type,
cartprod: $i > $i > $i ).
thf(decl_30,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_31,type,
esk1_2: $i > $i > $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
epred1_0: $i > $i > $o ).
thf(dpsetconstrSub,conjecture,
( dsetconstrEL
=> ( subsetI2
=> ! [X1: $i,X5: $i,X8: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X1 @ X5
@ ^ [X3: $i,X4: $i] : ( X8 @ X3 @ X4 ) )
@ ( cartprod @ X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CgfIfYDqqD/E---3.1_1720651.p',dpsetconstrSub) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CgfIfYDqqD/E---3.1_1720651.p',dsetconstrEL) ).
thf(dpsetconstr,axiom,
( dpsetconstr
= ( ^ [X1: $i,X5: $i,X6: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X5 )
@ ^ [X7: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X4: $i] :
( ( in @ X4 @ X5 )
& ( X6 @ X3 @ X4 )
& ( X7
= ( kpair @ X3 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CgfIfYDqqD/E---3.1_1720651.p',dpsetconstr) ).
thf(subsetI2,axiom,
( subsetI2
<=> ! [X1: $i,X5: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ X3 @ X5 ) )
=> ( subset @ X1 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CgfIfYDqqD/E---3.1_1720651.p',subsetI2) ).
thf(c_0_4,negated_conjecture,
~ ( dsetconstrEL
=> ( subsetI2
=> ! [X1: $i,X5: $i,X8: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X1 @ X5
@ ^ [X3: $i,X4: $i] : ( X8 @ X3 @ X4 ) )
@ ( cartprod @ X1 @ X5 ) ) ) ),
inference(assume_negation,[status(cth)],[dpsetconstrSub]) ).
thf(c_0_5,plain,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( in @ X3 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_6,plain,
( dpsetconstr
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Z0 @ Z1 )
@ ^ [Z3: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ? [X4: $i] :
( ( in @ X4 @ Z1 )
& ( Z2 @ X3 @ X4 )
& ( Z3
= ( kpair @ X3 @ X4 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstr]) ).
thf(c_0_7,negated_conjecture,
~ ( ! [X18: $i,X19: $i > $o,X20: $i] :
( ( in @ X20 @ ( dsetconstr @ X18 @ X19 ) )
=> ( in @ X20 @ X18 ) )
=> ( ! [X21: $i,X22: $i] :
( ! [X23: $i] :
( ( in @ X23 @ X21 )
=> ( in @ X23 @ X22 ) )
=> ( subset @ X21 @ X22 ) )
=> ! [X1: $i,X5: $i,X8: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X5 )
@ ^ [Z0: $i] :
? [X24: $i] :
( ( in @ X24 @ X1 )
& ? [X25: $i] :
( ( in @ X25 @ X5 )
& ( X8 @ X24 @ X25 )
& ( Z0
= ( kpair @ X24 @ X25 ) ) ) ) )
@ ( cartprod @ X1 @ X5 ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4]),c_0_5]),c_0_6]),subsetI2])]) ).
thf(c_0_8,negated_conjecture,
! [X26: $i,X27: $i > $o,X28: $i,X29: $i,X30: $i] :
( ( ~ ( in @ X28 @ ( dsetconstr @ X26 @ X27 ) )
| ( in @ X28 @ X26 ) )
& ( ( in @ ( esk1_2 @ X29 @ X30 ) @ X29 )
| ( subset @ X29 @ X30 ) )
& ( ~ ( in @ ( esk1_2 @ X29 @ X30 ) @ X30 )
| ( subset @ X29 @ X30 ) )
& ~ ( subset
@ ( dsetconstr @ ( cartprod @ esk2_0 @ esk3_0 )
@ ^ [Z0: $i] :
? [X24: $i] :
( ( in @ X24 @ esk2_0 )
& ? [X25: $i] :
( ( in @ X25 @ esk3_0 )
& ( epred1_0 @ X24 @ X25 )
& ( Z0
= ( kpair @ X24 @ X25 ) ) ) ) )
@ ( cartprod @ esk2_0 @ esk3_0 ) ) ),
inference(distribute,[status(thm)],[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_7])])])])])]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X3: $i] :
( ( in @ ( esk1_2 @ X1 @ X3 ) @ X1 )
| ( subset @ X1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i] :
( ( subset @ X1 @ X3 )
| ~ ( in @ ( esk1_2 @ X1 @ X3 ) @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ ( esk1_2 @ ( dsetconstr @ X1 @ X2 ) @ X3 ) @ X1 )
| ( subset @ ( dsetconstr @ X1 @ X2 ) @ X3 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( subset
@ ( dsetconstr @ ( cartprod @ esk2_0 @ esk3_0 )
@ ^ [Z0: $i] :
? [X35: $i] :
( ( in @ X35 @ esk2_0 )
& ? [X36: $i] :
( ( in @ X36 @ esk3_0 )
& ( epred1_0 @ X35 @ X36 )
& ( Z0
= ( kpair @ X35 @ X36 ) ) ) ) )
@ ( cartprod @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i > $o,X1: $i] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_13,c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU666^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 14:06:26 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.CgfIfYDqqD/E---3.1_1720651.p
% 0.07/0.25 % Version: 3.5.1-ho
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % Starting pre_casc_5 with 300s (1) cores
% 0.07/0.25 % Starting additional_ho_6 with 300s (1) cores
% 0.07/0.25 % ehoh_best_sine_rwall with pid 1720665 completed with status 0
% 0.07/0.25 % Result found by ehoh_best_sine_rwall
% 0.07/0.25 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.07/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.07/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.25 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.25 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.25 % Search class: HGUNF-FFSF22-DHSFMFBN
% 0.07/0.25 % partial match(3): HGUNF-FFSF22-SHSSMMBN
% 0.07/0.25 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.25 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.25 % SubtermCWHack with pid 1720668 completed with status 0
% 0.07/0.25 % Result found by SubtermCWHack
% 0.07/0.26 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.07/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.07/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.07/0.26 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.07/0.26 % Search class: HGUNF-FFSF22-DHSFMFBN
% 0.07/0.26 % partial match(3): HGUNF-FFSF22-SHSSMMBN
% 0.07/0.26 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.26 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.26 % Preprocessing time : 0.001 s
% 0.07/0.26
% 0.07/0.26 % Proof found!
% 0.07/0.26 % SZS status Theorem
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26 % Parsed axioms : 12
% 0.07/0.26 % Removed by relevancy pruning/SinE : 8
% 0.07/0.26 % Initial clauses : 4
% 0.07/0.26 % Removed in clause preprocessing : 0
% 0.07/0.26 % Initial clauses in saturation : 4
% 0.07/0.26 % Processed clauses : 11
% 0.07/0.26 % ...of these trivial : 0
% 0.07/0.26 % ...subsumed : 0
% 0.07/0.26 % ...remaining for further processing : 11
% 0.07/0.26 % Other redundant clauses eliminated : 0
% 0.07/0.26 % Clauses deleted for lack of memory : 0
% 0.07/0.26 % Backward-subsumed : 0
% 0.07/0.26 % Backward-rewritten : 0
% 0.07/0.26 % Generated clauses : 9
% 0.07/0.26 % ...of the previous two non-redundant : 8
% 0.07/0.26 % ...aggressively subsumed : 0
% 0.07/0.26 % Contextual simplify-reflections : 0
% 0.07/0.26 % Paramodulations : 9
% 0.07/0.26 % Factorizations : 0
% 0.07/0.26 % NegExts : 0
% 0.07/0.26 % Equation resolutions : 0
% 0.07/0.26 % Disequality decompositions : 0
% 0.07/0.26 % Total rewrite steps : 0
% 0.07/0.26 % ...of those cached : 0
% 0.07/0.26 % Propositional unsat checks : 0
% 0.07/0.26 % Propositional check models : 0
% 0.07/0.26 % Propositional check unsatisfiable : 0
% 0.07/0.26 % Propositional clauses : 0
% 0.07/0.26 % Propositional clauses after purity: 0
% 0.07/0.26 % Propositional unsat core size : 0
% 0.07/0.26 % Propositional preprocessing time : 0.000
% 0.07/0.26 % Propositional encoding time : 0.000
% 0.07/0.26 % Propositional solver time : 0.000
% 0.07/0.26 % Success case prop preproc time : 0.000
% 0.07/0.26 % Success case prop encoding time : 0.000
% 0.07/0.26 % Success case prop solver time : 0.000
% 0.07/0.26 % Current number of processed clauses : 11
% 0.07/0.26 % Positive orientable unit clauses : 4
% 0.07/0.26 % Positive unorientable unit clauses: 0
% 0.07/0.26 % Negative unit clauses : 1
% 0.07/0.26 % Non-unit-clauses : 6
% 0.07/0.26 % Current number of unprocessed clauses: 1
% 0.07/0.26 % ...number of literals in the above : 2
% 0.07/0.26 % Current number of archived formulas : 0
% 0.07/0.26 % Current number of archived clauses : 0
% 0.07/0.26 % Clause-clause subsumption calls (NU) : 16
% 0.07/0.26 % Rec. Clause-clause subsumption calls : 10
% 0.07/0.26 % Non-unit clause-clause subsumptions : 0
% 0.07/0.26 % Unit Clause-clause subsumption calls : 14
% 0.07/0.26 % Rewrite failures with RHS unbound : 0
% 0.07/0.26 % BW rewrite match attempts : 6
% 0.07/0.26 % BW rewrite match successes : 0
% 0.07/0.26 % Condensation attempts : 0
% 0.07/0.26 % Condensation successes : 0
% 0.07/0.26 % Termbank termtop insertions : 1014
% 0.07/0.26 % Search garbage collected termcells : 317
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.005 s
% 0.07/0.26 % System time : 0.001 s
% 0.07/0.26 % Total time : 0.006 s
% 0.07/0.26 % Maximum resident set size: 3644 pages
% 0.07/0.26
% 0.07/0.26 % -------------------------------------------------
% 0.07/0.26 % User time : 0.008 s
% 0.07/0.26 % System time : 0.004 s
% 0.07/0.26 % Total time : 0.012 s
% 0.07/0.26 % Maximum resident set size: 4608 pages
% 0.07/0.26 % E exiting
%------------------------------------------------------------------------------