%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU778^2 : 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 : n017.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 0.09s 0.24s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 8 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 202 ( 4 ~; 0 |; 13 &; 174 @)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 60 ( 34 ^; 21 !; 5 ?; 60 :)
% 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,
breln1: $i > $i > $o ).
thf(decl_30,type,
setOfPairsIsBReln1: $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(breln1,axiom,
( breln1
= ( ^ [X1: $i,X4: $i] : ( breln @ X1 @ X1 @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TqAoTpseIc/E---3.1_409515.p',breln1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TqAoTpseIc/E---3.1_409515.p',breln) ).
thf(setOfPairsIsBReln1,axiom,
( setOfPairsIsBReln1
<=> ! [X1: $i,X5: $i > $i > $o] :
( breln1 @ X1
@ ( dpsetconstr @ X1 @ X1
@ ^ [X6: $i,X7: $i] : ( X5 @ X6 @ X7 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TqAoTpseIc/E---3.1_409515.p',setOfPairsIsBReln1) ).
thf(breln1compprop,conjecture,
( setOfPairsIsBReln1
=> ! [X1: $i,X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ! [X8: $i] :
( ( breln1 @ X1 @ X8 )
=> ( breln1 @ X1 @ ( breln1compset @ X1 @ X4 @ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TqAoTpseIc/E---3.1_409515.p',breln1compprop) ).
thf(breln1compset,axiom,
( breln1compset
= ( ^ [X1: $i,X4: $i,X8: $i] :
( dpsetconstr @ X1 @ X1
@ ^ [X6: $i,X7: $i] :
? [X9: $i] :
( ( in @ X9 @ X1 )
& ( in @ ( kpair @ X6 @ X9 ) @ X4 )
& ( in @ ( kpair @ X9 @ X7 ) @ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TqAoTpseIc/E---3.1_409515.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,plain,
( setOfPairsIsBReln1
<=> ! [X1: $i,X5: $i > $i > $o] :
( breln1 @ X1
@ ( dpsetconstr @ X1 @ X1
@ ^ [Z0: $i,Z1: $i] : ( X5 @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1]) ).
thf(c_0_8,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_9,negated_conjecture,
~ ( setOfPairsIsBReln1
=> ! [X1: $i,X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ! [X8: $i] :
( ( breln1 @ X1 @ X8 )
=> ( breln1 @ X1 @ ( breln1compset @ X1 @ X4 @ X8 ) ) ) ) ),
inference(assume_negation,[status(cth)],[breln1compprop]) ).
thf(c_0_10,plain,
( breln1compset
= ( ^ [Z0: $i,Z1: $i,Z2: $i] :
( dpsetconstr @ Z0 @ Z0
@ ^ [Z3: $i,Z4: $i] :
? [X9: $i] :
( ( in @ X9 @ Z0 )
& ( in @ ( kpair @ Z3 @ X9 ) @ Z1 )
& ( in @ ( kpair @ X9 @ Z4 ) @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[breln1compset]) ).
thf(c_0_11,plain,
( setOfPairsIsBReln1
= ( ! [X1: $i,X5: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X1 @ X1
@ ^ [Z0: $i,Z1: $i] : ( X5 @ Z0 @ Z1 ) )
@ ( cartprod @ X1 @ X1 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_12,negated_conjecture,
~ ( ! [X15: $i,X16: $i > $i > $o] : ( subset @ ( dpsetconstr @ X15 @ X15 @ X16 ) @ ( cartprod @ X15 @ X15 ) )
=> ! [X1: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X1 ) )
=> ! [X8: $i] :
( ( subset @ X8 @ ( cartprod @ X1 @ X1 ) )
=> ( subset
@ ( dpsetconstr @ X1 @ X1
@ ^ [Z0: $i,Z1: $i] :
? [X17: $i] :
( ( in @ X17 @ X1 )
& ( in @ ( kpair @ Z0 @ X17 ) @ X4 )
& ( in @ ( kpair @ X17 @ Z1 ) @ X8 ) ) )
@ ( cartprod @ X1 @ X1 ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_8])]) ).
thf(c_0_13,negated_conjecture,
! [X18: $i,X19: $i > $i > $o] :
( ( subset @ ( dpsetconstr @ X18 @ X18 @ X19 ) @ ( cartprod @ X18 @ X18 ) )
& ( subset @ esk2_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ( subset @ esk3_0 @ ( cartprod @ esk1_0 @ esk1_0 ) )
& ~ ( subset
@ ( dpsetconstr @ esk1_0 @ esk1_0
@ ^ [Z0: $i,Z1: $i] :
? [X17: $i] :
( ( in @ X17 @ esk1_0 )
& ( in @ ( kpair @ Z0 @ X17 ) @ esk2_0 )
& ( in @ ( kpair @ X17 @ Z1 ) @ esk3_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_12])])])])]) ).
thf(c_0_14,negated_conjecture,
~ ( subset
@ ( dpsetconstr @ esk1_0 @ esk1_0
@ ^ [Z0: $i,Z1: $i] :
? [X23: $i] :
( ( in @ X23 @ esk1_0 )
& ( in @ ( kpair @ Z0 @ X23 ) @ esk2_0 )
& ( in @ ( kpair @ X23 @ Z1 ) @ esk3_0 ) ) )
@ ( cartprod @ esk1_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X5: $i > $i > $o,X1: $i] : ( subset @ ( dpsetconstr @ X1 @ X1 @ X5 ) @ ( cartprod @ X1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_14,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU778^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:23:22 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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.TqAoTpseIc/E---3.1_409515.p
% 0.09/0.24 % Version: 3.5.1-ho
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLMNSFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.09/0.24 % Starting lpo1_def_fix with 300s (1) cores
% 0.09/0.24 % sh5l with pid 409549 completed with status 0
% 0.09/0.24 % Result found by sh5l
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLMNSFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.24 % Search class: HUUNF-FFSF32-DSFFMFBN
% 0.09/0.24 % partial match(4): HGUNF-FFSF32-SFFFMFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % SubtermCWHack with pid 409552 completed with status 0
% 0.09/0.24 % Result found by SubtermCWHack
% 0.09/0.24 % Preprocessing class: HSSSSMSSSLMNSFN.
% 0.09/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.09/0.24 % Starting sh5l with 300s (1) cores
% 0.09/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.09/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.09/0.24 % Search class: HUUNF-FFSF32-DSFFMFBN
% 0.09/0.24 % partial match(4): HGUNF-FFSF32-SFFFMFNN
% 0.09/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.24 % Preprocessing time : 0.001 s
% 0.09/0.24
% 0.09/0.24 % Proof found!
% 0.09/0.24 % SZS status Theorem
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.24 % Parsed axioms : 14
% 0.09/0.24 % Removed by relevancy pruning/SinE : 9
% 0.09/0.24 % Initial clauses : 4
% 0.09/0.24 % Removed in clause preprocessing : 0
% 0.09/0.24 % Initial clauses in saturation : 4
% 0.09/0.24 % Processed clauses : 4
% 0.09/0.24 % ...of these trivial : 0
% 0.09/0.24 % ...subsumed : 0
% 0.09/0.24 % ...remaining for further processing : 4
% 0.09/0.24 % Other redundant clauses eliminated : 0
% 0.09/0.24 % Clauses deleted for lack of memory : 0
% 0.09/0.24 % Backward-subsumed : 0
% 0.09/0.24 % Backward-rewritten : 0
% 0.09/0.24 % Generated clauses : 1
% 0.09/0.24 % ...of the previous two non-redundant : 0
% 0.09/0.24 % ...aggressively subsumed : 0
% 0.09/0.24 % Contextual simplify-reflections : 0
% 0.09/0.24 % Paramodulations : 1
% 0.09/0.24 % Factorizations : 0
% 0.09/0.24 % NegExts : 0
% 0.09/0.24 % Equation resolutions : 0
% 0.09/0.24 % Disequality decompositions : 0
% 0.09/0.24 % Total rewrite steps : 0
% 0.09/0.24 % ...of those cached : 0
% 0.09/0.24 % Propositional unsat checks : 0
% 0.09/0.24 % Propositional check models : 0
% 0.09/0.24 % Propositional check unsatisfiable : 0
% 0.09/0.24 % Propositional clauses : 0
% 0.09/0.24 % Propositional clauses after purity: 0
% 0.09/0.24 % Propositional unsat core size : 0
% 0.09/0.24 % Propositional preprocessing time : 0.000
% 0.09/0.24 % Propositional encoding time : 0.000
% 0.09/0.24 % Propositional solver time : 0.000
% 0.09/0.24 % Success case prop preproc time : 0.000
% 0.09/0.24 % Success case prop encoding time : 0.000
% 0.09/0.24 % Success case prop solver time : 0.000
% 0.09/0.24 % Current number of processed clauses : 4
% 0.09/0.24 % Positive orientable unit clauses : 3
% 0.09/0.24 % Positive unorientable unit clauses: 0
% 0.09/0.24 % Negative unit clauses : 1
% 0.09/0.24 % Non-unit-clauses : 0
% 0.09/0.24 % Current number of unprocessed clauses: 0
% 0.09/0.24 % ...number of literals in the above : 0
% 0.09/0.24 % Current number of archived formulas : 0
% 0.09/0.24 % Current number of archived clauses : 0
% 0.09/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.24 % Non-unit clause-clause subsumptions : 0
% 0.09/0.24 % Unit Clause-clause subsumption calls : 0
% 0.09/0.24 % Rewrite failures with RHS unbound : 0
% 0.09/0.24 % BW rewrite match attempts : 0
% 0.09/0.24 % BW rewrite match successes : 0
% 0.09/0.24 % Condensation attempts : 0
% 0.09/0.24 % Condensation successes : 0
% 0.09/0.24 % Termbank termtop insertions : 658
% 0.09/0.24 % Search garbage collected termcells : 195
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.004 s
% 0.09/0.24 % System time : 0.000 s
% 0.09/0.24 % Total time : 0.005 s
% 0.09/0.24 % Maximum resident set size: 3588 pages
% 0.09/0.24
% 0.09/0.24 % -------------------------------------------------
% 0.09/0.24 % User time : 0.007 s
% 0.09/0.24 % System time : 0.004 s
% 0.09/0.24 % Total time : 0.011 s
% 0.09/0.24 % Maximum resident set size: 4864 pages
% 0.09/0.24 % E exiting
%------------------------------------------------------------------------------