%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU773^2 : 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 : n001.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 08:25:34 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 122 ( 6 equ; 0 cnn)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 531 ( 39 ~; 40 |; 7 &; 405 @)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 75 ( 12 ^; 63 !; 0 ?; 75 :)
% 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,
subbreln: $o ).
thf(decl_29,type,
breln1: $i > $i > $o ).
thf(decl_30,type,
esk1_4: $i > $i > $i > $i > $i ).
thf(decl_31,type,
esk2_4: $i > $i > $i > $i > $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(decl_34,type,
esk5_0: $i ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F5h0Ptqbue/E---3.1_1324656.p',breln) ).
thf(breln1,axiom,
( breln1
= ( ^ [X1: $i,X4: $i] : ( breln @ X1 @ X1 @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F5h0Ptqbue/E---3.1_1324656.p',breln1) ).
thf(subbreln1,conjecture,
( subbreln
=> ! [X1: $i,X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ! [X5: $i] :
( ( breln1 @ X1 @ X5 )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( subset @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F5h0Ptqbue/E---3.1_1324656.p',subbreln1) ).
thf(subbreln,axiom,
( subbreln
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i] :
( ( breln @ X1 @ X2 @ X5 )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( subset @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F5h0Ptqbue/E---3.1_1324656.p',subbreln) ).
thf(c_0_4,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
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,negated_conjecture,
~ ( subbreln
=> ! [X1: $i,X4: $i] :
( ( breln1 @ X1 @ X4 )
=> ! [X5: $i] :
( ( breln1 @ X1 @ X5 )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( subset @ X4 @ X5 ) ) ) ) ),
inference(assume_negation,[status(cth)],[subbreln1]) ).
thf(c_0_7,axiom,
( subbreln
= ( ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ! [X5: $i] :
( ( subset @ X5 @ ( cartprod @ X1 @ X2 ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( subset @ X4 @ X5 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[subbreln,c_0_4]) ).
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_4]) ).
thf(c_0_9,negated_conjecture,
~ ( ! [X19: $i,X20: $i,X21: $i] :
( ( subset @ X21 @ ( cartprod @ X19 @ X20 ) )
=> ! [X22: $i] :
( ( subset @ X22 @ ( cartprod @ X19 @ X20 ) )
=> ( ! [X23: $i] :
( ( in @ X23 @ X19 )
=> ! [X24: $i] :
( ( in @ X24 @ X20 )
=> ( ( in @ ( kpair @ X23 @ X24 ) @ X21 )
=> ( in @ ( kpair @ X23 @ X24 ) @ X22 ) ) ) )
=> ( subset @ X21 @ X22 ) ) ) )
=> ! [X1: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X1 ) )
=> ! [X5: $i] :
( ( subset @ X5 @ ( cartprod @ X1 @ X1 ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X5 ) ) ) )
=> ( subset @ X4 @ X5 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X25: $i,X26: $i,X27: $i,X28: $i,X34: $i,X35: $i] :
( ( ( in @ ( esk1_4 @ X25 @ X26 @ X27 @ X28 ) @ X25 )
| ( subset @ X27 @ X28 )
| ~ ( subset @ X28 @ ( cartprod @ X25 @ X26 ) )
| ~ ( subset @ X27 @ ( cartprod @ X25 @ X26 ) ) )
& ( ( in @ ( esk2_4 @ X25 @ X26 @ X27 @ X28 ) @ X26 )
| ( subset @ X27 @ X28 )
| ~ ( subset @ X28 @ ( cartprod @ X25 @ X26 ) )
| ~ ( subset @ X27 @ ( cartprod @ X25 @ X26 ) ) )
& ( ( in @ ( kpair @ ( esk1_4 @ X25 @ X26 @ X27 @ X28 ) @ ( esk2_4 @ X25 @ X26 @ X27 @ X28 ) ) @ X27 )
| ( subset @ X27 @ X28 )
| ~ ( subset @ X28 @ ( cartprod @ X25 @ X26 ) )
| ~ ( subset @ X27 @ ( cartprod @ X25 @ X26 ) ) )
& ( ~ ( in @ ( kpair @ ( esk1_4 @ X25 @ X26 @ X27 @ X28 ) @ ( esk2_4 @ X25 @ X26 @ X27 @ X28 ) ) @ X28 )
| ( subset @ X27 @ X28 )
| ~ ( subset @ X28 @ ( cartprod @ X25 @ X26 ) )
| ~ ( subset @ X27 @ ( cartprod @ X25 @ X26 ) ) )
& ( subset @ esk4_0 @ ( cartprod @ esk3_0 @ esk3_0 ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk3_0 ) )
& ( ~ ( in @ X34 @ esk3_0 )
| ~ ( in @ X35 @ esk3_0 )
| ~ ( in @ ( kpair @ X34 @ X35 ) @ esk4_0 )
| ( in @ ( kpair @ X34 @ X35 ) @ esk5_0 ) )
& ~ ( subset @ esk4_0 @ esk5_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_9])])])])])]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( in @ ( kpair @ X1 @ X2 ) @ esk5_0 )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X2 @ esk3_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X3 )
| ( subset @ X3 @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( subset @ X3 @ X4 )
| ~ ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) ) @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ esk4_0 @ X3 ) @ ( esk2_4 @ X1 @ X2 @ esk4_0 @ X3 ) ) @ esk5_0 )
| ( subset @ esk4_0 @ X3 )
| ~ ( in @ ( esk2_4 @ X1 @ X2 @ esk4_0 @ X3 ) @ esk3_0 )
| ~ ( in @ ( esk1_4 @ X1 @ X2 @ esk4_0 @ X3 ) @ esk3_0 )
| ~ ( subset @ esk4_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_15,negated_conjecture,
~ ( subset @ esk4_0 @ esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i] :
( ~ ( in @ ( esk2_4 @ X1 @ X2 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( in @ ( esk1_4 @ X1 @ X2 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ esk4_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X4 ) @ X2 )
| ( subset @ X3 @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i] :
( ~ ( in @ ( esk1_4 @ X1 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ esk3_0 ) )
| ~ ( subset @ esk4_0 @ ( cartprod @ X1 @ esk3_0 ) ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X4 ) @ X1 )
| ( subset @ X3 @ X4 )
| ~ ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_20,negated_conjecture,
subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_21,negated_conjecture,
subset @ esk4_0 @ ( cartprod @ esk3_0 @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU773^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n001.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:32:05 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 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.F5h0Ptqbue/E---3.1_1324656.p
% 0.10/0.25 % Version: 3.5.1-ho
% 0.10/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.25 % Starting sh4l with 300s (1) cores
% 0.10/0.25 % Starting ho_unfolding_2 with 300s (1) cores
% 0.10/0.25 % sh4l with pid 1324671 completed with status 0
% 0.10/0.25 % Result found by sh4l
% 0.10/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.25 % Starting sh4l with 300s (1) cores
% 0.10/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HGUNF-FFSF33-SSFFMFNN
% 0.10/0.25 % partial match(2): HGUNF-FFSF32-SFFFMFNN
% 0.10/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.25 % SubtermCWHack with pid 1324673 completed with status 0
% 0.10/0.25 % Result found by SubtermCWHack
% 0.10/0.25 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.10/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.25 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.10/0.25 % Starting post_as_ho5 with 300s (1) cores
% 0.10/0.25 % Starting sh4l with 300s (1) cores
% 0.10/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.25 % No SInE strategy applied
% 0.10/0.25 % Search class: HGUNF-FFSF33-SSFFMFNN
% 0.10/0.25 % partial match(2): HGUNF-FFSF32-SFFFMFNN
% 0.10/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.25 % Preprocessing time : 0.001 s
% 0.10/0.25
% 0.10/0.25 % Proof found!
% 0.10/0.25 % SZS status Theorem
% 0.10/0.25 % SZS output start CNFRefutation
% See solution above
% 0.10/0.25 % Parsed axioms : 11
% 0.10/0.25 % Removed by relevancy pruning/SinE : 0
% 0.10/0.25 % Initial clauses : 15
% 0.10/0.25 % Removed in clause preprocessing : 7
% 0.10/0.25 % Initial clauses in saturation : 8
% 0.10/0.25 % Processed clauses : 14
% 0.10/0.25 % ...of these trivial : 0
% 0.10/0.25 % ...subsumed : 0
% 0.10/0.25 % ...remaining for further processing : 14
% 0.10/0.25 % Other redundant clauses eliminated : 0
% 0.10/0.25 % Clauses deleted for lack of memory : 0
% 0.10/0.25 % Backward-subsumed : 0
% 0.10/0.25 % Backward-rewritten : 0
% 0.10/0.25 % Generated clauses : 7
% 0.10/0.25 % ...of the previous two non-redundant : 6
% 0.10/0.25 % ...aggressively subsumed : 0
% 0.10/0.25 % Contextual simplify-reflections : 0
% 0.10/0.25 % Paramodulations : 7
% 0.10/0.25 % Factorizations : 0
% 0.10/0.25 % NegExts : 0
% 0.10/0.25 % Equation resolutions : 0
% 0.10/0.25 % Disequality decompositions : 0
% 0.10/0.25 % Total rewrite steps : 2
% 0.10/0.25 % ...of those cached : 0
% 0.10/0.25 % Propositional unsat checks : 0
% 0.10/0.25 % Propositional check models : 0
% 0.10/0.25 % Propositional check unsatisfiable : 0
% 0.10/0.25 % Propositional clauses : 0
% 0.10/0.25 % Propositional clauses after purity: 0
% 0.10/0.25 % Propositional unsat core size : 0
% 0.10/0.25 % Propositional preprocessing time : 0.000
% 0.10/0.25 % Propositional encoding time : 0.000
% 0.10/0.25 % Propositional solver time : 0.000
% 0.10/0.25 % Success case prop preproc time : 0.000
% 0.10/0.25 % Success case prop encoding time : 0.000
% 0.10/0.25 % Success case prop solver time : 0.000
% 0.10/0.25 % Current number of processed clauses : 14
% 0.10/0.25 % Positive orientable unit clauses : 4
% 0.10/0.25 % Positive unorientable unit clauses: 0
% 0.10/0.25 % Negative unit clauses : 1
% 0.10/0.25 % Non-unit-clauses : 9
% 0.10/0.25 % Current number of unprocessed clauses: 0
% 0.10/0.25 % ...number of literals in the above : 0
% 0.10/0.25 % Current number of archived formulas : 0
% 0.10/0.25 % Current number of archived clauses : 0
% 0.10/0.25 % Clause-clause subsumption calls (NU) : 30
% 0.10/0.25 % Rec. Clause-clause subsumption calls : 10
% 0.10/0.25 % Non-unit clause-clause subsumptions : 0
% 0.10/0.25 % Unit Clause-clause subsumption calls : 6
% 0.10/0.25 % Rewrite failures with RHS unbound : 0
% 0.10/0.25 % BW rewrite match attempts : 0
% 0.10/0.25 % BW rewrite match successes : 0
% 0.10/0.25 % Condensation attempts : 0
% 0.10/0.25 % Condensation successes : 0
% 0.10/0.25 % Termbank termtop insertions : 1560
% 0.10/0.25 % Search garbage collected termcells : 402
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.005 s
% 0.10/0.25 % System time : 0.001 s
% 0.10/0.25 % Total time : 0.006 s
% 0.10/0.25 % Maximum resident set size: 3636 pages
% 0.10/0.25
% 0.10/0.25 % -------------------------------------------------
% 0.10/0.25 % User time : 0.008 s
% 0.10/0.25 % System time : 0.005 s
% 0.10/0.25 % Total time : 0.012 s
% 0.10/0.25 % Maximum resident set size: 4864 pages
% 0.10/0.25 % E exiting
%------------------------------------------------------------------------------