%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU667^2 : 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 : n016.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 0.24s 0.26s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 14 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 215 ( 4 ~; 0 |; 28 &; 178 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 74 ( 29 ^; 27 !; 18 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
subset: $i > $i > $o ).
thf(decl_26,type,
kpair: $i > $i > $i ).
thf(decl_27,type,
cartprod: $i > $i > $i ).
thf(decl_28,type,
breln: $i > $i > $i > $o ).
thf(decl_29,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_30,type,
dpsetconstrSub: $o ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
epred1_0: $i > $i > $o ).
thf(dpsetconstrSub,axiom,
( dpsetconstrSub
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [X6: $i,X7: $i] : ( X4 @ X6 @ X7 ) )
@ ( cartprod @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i9gsPEfTGa/E---3.1_410314.p',dpsetconstrSub) ).
thf(dpsetconstr,axiom,
( dpsetconstr
= ( ^ [X1: $i,X2: $i,X4: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [X5: $i] :
? [X6: $i] :
( ( in @ X6 @ X1 )
& ? [X7: $i] :
( ( in @ X7 @ X2 )
& ( X4 @ X6 @ X7 )
& ( X5
= ( kpair @ X6 @ X7 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i9gsPEfTGa/E---3.1_410314.p',dpsetconstr) ).
thf(setOfPairsIsBReln,conjecture,
( dpsetconstrSub
=> ! [X1: $i,X2: $i,X4: $i > $i > $o] :
( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [X6: $i,X7: $i] : ( X4 @ X6 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i9gsPEfTGa/E---3.1_410314.p',setOfPairsIsBReln) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i9gsPEfTGa/E---3.1_410314.p',breln) ).
thf(c_0_4,plain,
( dpsetconstrSub
<=> ! [X1: $i,X2: $i,X4: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X1 @ X2
@ ^ [Z0: $i,Z1: $i] : ( X4 @ Z0 @ Z1 ) )
@ ( cartprod @ X1 @ X2 ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).
thf(c_0_5,plain,
( dpsetconstr
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Z0 @ Z1 )
@ ^ [Z3: $i] :
? [X6: $i] :
( ( in @ X6 @ Z0 )
& ? [X7: $i] :
( ( in @ X7 @ Z1 )
& ( Z2 @ X6 @ X7 )
& ( Z3
= ( kpair @ X6 @ X7 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstr]) ).
thf(c_0_6,negated_conjecture,
~ ( dpsetconstrSub
=> ! [X1: $i,X2: $i,X4: $i > $i > $o] :
( breln @ X1 @ X2
@ ( dpsetconstr @ X1 @ X2
@ ^ [X6: $i,X7: $i] : ( X4 @ X6 @ X7 ) ) ) ),
inference(assume_negation,[status(cth)],[setOfPairsIsBReln]) ).
thf(c_0_7,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_8,plain,
( dpsetconstrSub
= ( ! [X1: $i,X2: $i,X4: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Z0: $i] :
? [X14: $i] :
( ( in @ X14 @ X1 )
& ? [X15: $i] :
( ( in @ X15 @ X2 )
& ( X4 @ X14 @ X15 )
& ( Z0
= ( kpair @ X14 @ X15 ) ) ) ) )
@ ( cartprod @ X1 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_4,c_0_5]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X16: $i,X17: $i,X18: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X16 @ X17 )
@ ^ [Z0: $i] :
? [X19: $i] :
( ( in @ X19 @ X16 )
& ? [X20: $i] :
( ( in @ X20 @ X17 )
& ( X18 @ X19 @ X20 )
& ( Z0
= ( kpair @ X19 @ X20 ) ) ) ) )
@ ( cartprod @ X16 @ X17 ) )
=> ! [X1: $i,X2: $i,X4: $i > $i > $o] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Z0: $i] :
? [X21: $i] :
( ( in @ X21 @ X1 )
& ? [X22: $i] :
( ( in @ X22 @ X2 )
& ( X4 @ X21 @ X22 )
& ( Z0
= ( kpair @ X21 @ X22 ) ) ) ) )
@ ( cartprod @ X1 @ X2 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6]),c_0_7]),c_0_5]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X23: $i,X24: $i,X25: $i > $i > $o] :
( ( subset
@ ( dsetconstr @ ( cartprod @ X23 @ X24 )
@ ^ [Z0: $i] :
? [X19: $i] :
( ( in @ X19 @ X23 )
& ? [X20: $i] :
( ( in @ X20 @ X24 )
& ( X25 @ X19 @ X20 )
& ( Z0
= ( kpair @ X19 @ X20 ) ) ) ) )
@ ( cartprod @ X23 @ X24 ) )
& ~ ( subset
@ ( dsetconstr @ ( cartprod @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
? [X21: $i] :
( ( in @ X21 @ esk1_0 )
& ? [X22: $i] :
( ( in @ X22 @ esk2_0 )
& ( epred1_0 @ X21 @ X22 )
& ( Z0
= ( kpair @ X21 @ X22 ) ) ) ) )
@ ( cartprod @ 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_9])])])])]) ).
thf(c_0_11,negated_conjecture,
~ ( subset
@ ( 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 ) ) ) ) )
@ ( cartprod @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X4: $i > $i > $o,X2: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ X1 @ X2 )
@ ^ [Z0: $i] :
? [X31: $i] :
( ( in @ X31 @ X1 )
& ? [X32: $i] :
( ( in @ X32 @ X2 )
& ( X4 @ X31 @ X32 )
& ( Z0
= ( kpair @ X31 @ X32 ) ) ) ) )
@ ( cartprod @ X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU667^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:11:34 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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.i9gsPEfTGa/E---3.1_410314.p
% 0.24/0.26 % Version: 3.5.1-ho
% 0.24/0.26 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.24/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.24/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.26 % Starting sh2l with 300s (1) cores
% 0.24/0.26 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.24/0.26 % ehoh_best_nonlift_rwall with pid 410350 completed with status 0
% 0.24/0.26 % Result found by ehoh_best_nonlift_rwall
% 0.24/0.26 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.24/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.24/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.26 % Starting sh2l with 300s (1) cores
% 0.24/0.26 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.24/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.24/0.26 % No SInE strategy applied
% 0.24/0.26 % Search class: HUUNF-FFSF22-DHSFMFBN
% 0.24/0.26 % partial match(3): HUUNF-FFSF00-SHSFMFBN
% 0.24/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.26 % SubtermCWHack with pid 410351 completed with status 0
% 0.24/0.26 % Result found by SubtermCWHack
% 0.24/0.26 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.24/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.26 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.24/0.26 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.24/0.26 % Starting sh2l with 300s (1) cores
% 0.24/0.26 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.24/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.24/0.26 % No SInE strategy applied
% 0.24/0.26 % Search class: HUUNF-FFSF22-DHSFMFBN
% 0.24/0.26 % partial match(3): HUUNF-FFSF00-SHSFMFBN
% 0.24/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.26 % Preprocessing time : 0.001 s
% 0.24/0.26
% 0.24/0.26 % Proof found!
% 0.24/0.26 % SZS status Theorem
% 0.24/0.26 % SZS output start CNFRefutation
% See solution above
% 0.24/0.26 % Parsed axioms : 12
% 0.24/0.26 % Removed by relevancy pruning/SinE : 0
% 0.24/0.26 % Initial clauses : 10
% 0.24/0.26 % Removed in clause preprocessing : 8
% 0.24/0.26 % Initial clauses in saturation : 2
% 0.24/0.26 % Processed clauses : 2
% 0.24/0.26 % ...of these trivial : 0
% 0.24/0.26 % ...subsumed : 0
% 0.24/0.26 % ...remaining for further processing : 1
% 0.24/0.26 % Other redundant clauses eliminated : 0
% 0.24/0.26 % Clauses deleted for lack of memory : 0
% 0.24/0.26 % Backward-subsumed : 0
% 0.24/0.26 % Backward-rewritten : 0
% 0.24/0.26 % Generated clauses : 0
% 0.24/0.26 % ...of the previous two non-redundant : 0
% 0.24/0.26 % ...aggressively subsumed : 0
% 0.24/0.26 % Contextual simplify-reflections : 0
% 0.24/0.26 % Paramodulations : 0
% 0.24/0.26 % Factorizations : 0
% 0.24/0.26 % NegExts : 0
% 0.24/0.26 % Equation resolutions : 0
% 0.24/0.26 % Disequality decompositions : 0
% 0.24/0.26 % Total rewrite steps : 1
% 0.24/0.26 % ...of those cached : 0
% 0.24/0.26 % Propositional unsat checks : 0
% 0.24/0.26 % Propositional check models : 0
% 0.24/0.26 % Propositional check unsatisfiable : 0
% 0.24/0.26 % Propositional clauses : 0
% 0.24/0.26 % Propositional clauses after purity: 0
% 0.24/0.26 % Propositional unsat core size : 0
% 0.24/0.26 % Propositional preprocessing time : 0.000
% 0.24/0.26 % Propositional encoding time : 0.000
% 0.24/0.26 % Propositional solver time : 0.000
% 0.24/0.26 % Success case prop preproc time : 0.000
% 0.24/0.26 % Success case prop encoding time : 0.000
% 0.24/0.26 % Success case prop solver time : 0.000
% 0.24/0.26 % Current number of processed clauses : 1
% 0.24/0.26 % Positive orientable unit clauses : 1
% 0.24/0.26 % Positive unorientable unit clauses: 0
% 0.24/0.26 % Negative unit clauses : 0
% 0.24/0.26 % Non-unit-clauses : 0
% 0.24/0.26 % Current number of unprocessed clauses: 0
% 0.24/0.26 % ...number of literals in the above : 0
% 0.24/0.26 % Current number of archived formulas : 0
% 0.24/0.26 % Current number of archived clauses : 0
% 0.24/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.26 % Non-unit clause-clause subsumptions : 0
% 0.24/0.26 % Unit Clause-clause subsumption calls : 0
% 0.24/0.26 % Rewrite failures with RHS unbound : 0
% 0.24/0.26 % BW rewrite match attempts : 0
% 0.24/0.26 % BW rewrite match successes : 0
% 0.24/0.26 % Condensation attempts : 0
% 0.24/0.26 % Condensation successes : 0
% 0.24/0.26 % Termbank termtop insertions : 904
% 0.24/0.26 % Search garbage collected termcells : 252
% 0.24/0.26
% 0.24/0.26 % -------------------------------------------------
% 0.24/0.26 % User time : 0.004 s
% 0.24/0.26 % System time : 0.000 s
% 0.24/0.26 % Total time : 0.004 s
% 0.24/0.26 % Maximum resident set size: 3640 pages
% 0.24/0.26
% 0.24/0.26 % -------------------------------------------------
% 0.24/0.26 % User time : 0.005 s
% 0.24/0.26 % System time : 0.005 s
% 0.24/0.26 % Total time : 0.010 s
% 0.24/0.26 % Maximum resident set size: 4864 pages
% 0.24/0.26 % E exiting
%------------------------------------------------------------------------------