%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU669^2 : 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 : n019.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 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 7 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 217 ( 8 ~; 4 |; 18 &; 170 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 73 ( 17 ^; 46 !; 10 ?; 73 :)
% 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,
kpair: $i > $i > $i ).
thf(decl_27,type,
cartprod: $i > $i > $i ).
thf(decl_28,type,
cartprodpairmemEL: $o ).
thf(decl_29,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
epred1_0: $i > $i > $o ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(dpsetconstrEL1,conjecture,
( dsetconstrEL
=> ( cartprodpairmemEL
=> ! [X1: $i,X5: $i,X8: $i > $i > $o,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X5
@ ^ [X9: $i,X7: $i] : ( X8 @ X9 @ X7 ) ) )
=> ( in @ X3 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Y7CG12X1oo/E---3.1_826177.p',dpsetconstrEL1) ).
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/sandbox2/tmp/tmp.Y7CG12X1oo/E---3.1_826177.p',dpsetconstr) ).
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/sandbox2/tmp/tmp.Y7CG12X1oo/E---3.1_826177.p',dsetconstrEL) ).
thf(cartprodpairmemEL,axiom,
( cartprodpairmemEL
<=> ! [X1: $i,X5: $i,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X5 ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Y7CG12X1oo/E---3.1_826177.p',cartprodpairmemEL) ).
thf(c_0_4,negated_conjecture,
~ ( dsetconstrEL
=> ( cartprodpairmemEL
=> ! [X1: $i,X5: $i,X8: $i > $i > $o,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X5
@ ^ [X9: $i,X7: $i] : ( X8 @ X9 @ X7 ) ) )
=> ( in @ X3 @ X1 ) ) ) ),
inference(assume_negation,[status(cth)],[dpsetconstrEL1]) ).
thf(c_0_5,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_6,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_7,negated_conjecture,
~ ( ! [X22: $i,X23: $i > $o,X24: $i] :
( ( in @ X24 @ ( dsetconstr @ X22 @ X23 ) )
=> ( in @ X24 @ X22 ) )
=> ( ! [X25: $i,X26: $i,X27: $i,X28: $i] :
( ( in @ ( kpair @ X27 @ X28 ) @ ( cartprod @ X25 @ X26 ) )
=> ( in @ X27 @ X25 ) )
=> ! [X1: $i,X5: $i,X8: $i > $i > $o,X3: $i,X4: $i] :
( ( in @ ( kpair @ X3 @ X4 )
@ ( dsetconstr @ ( cartprod @ X1 @ X5 )
@ ^ [Z0: $i] :
? [X29: $i] :
( ( in @ X29 @ X1 )
& ? [X30: $i] :
( ( in @ X30 @ X5 )
& ( X8 @ X29 @ X30 )
& ( Z0
= ( kpair @ X29 @ X30 ) ) ) ) ) )
=> ( in @ X3 @ X1 ) ) ) ),
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]),cartprodpairmemEL]),c_0_6])]) ).
thf(c_0_8,negated_conjecture,
! [X31: $i,X32: $i > $o,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ~ ( in @ X33 @ ( dsetconstr @ X31 @ X32 ) )
| ( in @ X33 @ X31 ) )
& ( ~ ( in @ ( kpair @ X36 @ X37 ) @ ( cartprod @ X34 @ X35 ) )
| ( in @ X36 @ X34 ) )
& ( in @ ( kpair @ esk3_0 @ esk4_0 )
@ ( dsetconstr @ ( cartprod @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
? [X29: $i] :
( ( in @ X29 @ esk1_0 )
& ? [X30: $i] :
( ( in @ X30 @ esk2_0 )
& ( epred1_0 @ X29 @ X30 )
& ( Z0
= ( kpair @ X29 @ X30 ) ) ) ) ) )
& ~ ( in @ esk3_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_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,
( in @ ( kpair @ esk3_0 @ esk4_0 )
@ ( dsetconstr @ ( cartprod @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
? [X43: $i] :
( ( in @ X43 @ esk1_0 )
& ? [X44: $i] :
( ( in @ X44 @ esk2_0 )
& ( epred1_0 @ X43 @ X44 )
& ( Z0
= ( kpair @ X43 @ X44 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X5: $i] :
( ( in @ X1 @ X4 )
| ~ ( in @ ( kpair @ X1 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
in @ ( kpair @ esk3_0 @ esk4_0 ) @ ( cartprod @ esk1_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
~ ( in @ esk3_0 @ esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU669^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n019.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 14:07:17 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.Y7CG12X1oo/E---3.1_826177.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.10/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % Starting pre_casc_5 with 300s (1) cores
% 0.10/0.24 % Starting additional_ho_6 with 300s (1) cores
% 0.10/0.24 % ehoh_best_sine_rwall with pid 826191 completed with status 0
% 0.10/0.24 % Result found by ehoh_best_sine_rwall
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.10/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.24 % Search class: HHUNF-FFSF22-DHSFMFBN
% 0.10/0.24 % partial match(4): HGUNF-FFSF22-SHSSMMBN
% 0.10/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 826194 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNHSN.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.10/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.24 % Search class: HHUNF-FFSF22-DHSFMFBN
% 0.10/0.24 % partial match(4): HGUNF-FFSF22-SHSSMMBN
% 0.10/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 11
% 0.10/0.24 % Removed by relevancy pruning/SinE : 7
% 0.10/0.24 % Initial clauses : 4
% 0.10/0.24 % Removed in clause preprocessing : 0
% 0.10/0.24 % Initial clauses in saturation : 4
% 0.10/0.24 % Processed clauses : 5
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 5
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 0
% 0.10/0.24 % Backward-rewritten : 0
% 0.10/0.24 % Generated clauses : 2
% 0.10/0.24 % ...of the previous two non-redundant : 1
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 2
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 0
% 0.10/0.24 % Equation resolutions : 0
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 0
% 0.10/0.24 % ...of those cached : 0
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 5
% 0.10/0.24 % Positive orientable unit clauses : 2
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 1
% 0.10/0.24 % Non-unit-clauses : 2
% 0.10/0.24 % Current number of unprocessed clauses: 0
% 0.10/0.24 % ...number of literals in the above : 0
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 0
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 2
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 1
% 0.10/0.24 % Non-unit clause-clause subsumptions : 0
% 0.10/0.24 % Unit Clause-clause subsumption calls : 0
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 0
% 0.10/0.24 % BW rewrite match successes : 0
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 900
% 0.10/0.24 % Search garbage collected termcells : 333
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.002 s
% 0.10/0.24 % System time : 0.001 s
% 0.10/0.24 % Total time : 0.004 s
% 0.10/0.24 % Maximum resident set size: 3592 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.004 s
% 0.10/0.24 % System time : 0.006 s
% 0.10/0.24 % Total time : 0.009 s
% 0.10/0.24 % Maximum resident set size: 4864 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------