%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU682^2 : 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 : n012.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 08:27:12 AM UTC 2026
% Result : Theorem 0.08s 0.14s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 3 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 476 ( 32 ~; 41 |; 7 &; 356 @)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 91 ( 6 ^; 85 !; 0 ?; 91 :)
% 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,
brelnall1: $o ).
thf(decl_29,type,
esk1_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_30,type,
esk2_4: $i > $i > $i > ( $i > $o ) > $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(decl_33,type,
esk5_0: $i ).
thf(decl_34,type,
epred1_0: $i > $o ).
thf(decl_35,type,
esk6_0: $i ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJc1Bnqmp8/E---3.1_159540.p',breln) ).
thf(brelnall2,conjecture,
( brelnall1
=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJc1Bnqmp8/E---3.1_159540.p',brelnall2) ).
thf(brelnall1,axiom,
( brelnall1
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aJc1Bnqmp8/E---3.1_159540.p',brelnall1) ).
thf(c_0_3,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_4,negated_conjecture,
~ ( brelnall1
=> ! [X1: $i,X2: $i,X4: $i] :
( ( breln @ X1 @ X2 @ X4 )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
inference(assume_negation,[status(cth)],[brelnall2]) ).
thf(c_0_5,axiom,
( brelnall1
= ( ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[brelnall1,c_0_3]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i] :
( ( subset @ X24 @ ( cartprod @ X22 @ X23 ) )
=> ! [X25: $i > $o] :
( ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ! [X27: $i] :
( ( in @ X27 @ X23 )
=> ( ( in @ ( kpair @ X26 @ X27 ) @ X24 )
=> ( X25 @ ( kpair @ X26 @ X27 ) ) ) ) )
=> ! [X28: $i] :
( ( in @ X28 @ X24 )
=> ( X25 @ X28 ) ) ) )
=> ! [X1: $i,X2: $i,X4: $i] :
( ( subset @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ! [X5: $i > $o] :
( ! [X6: $i] :
( ( in @ X6 @ X1 )
=> ! [X7: $i] :
( ( in @ X7 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X4 )
=> ( X5 @ ( kpair @ X6 @ X7 ) ) ) ) )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( X5 @ X6 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_3]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X29: $i,X30: $i,X31: $i,X32: $i > $o,X35: $i,X40: $i,X41: $i] :
( ( ( in @ ( esk1_4 @ X29 @ X30 @ X31 @ X32 ) @ X29 )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( in @ ( esk2_4 @ X29 @ X30 @ X31 @ X32 ) @ X30 )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( in @ ( kpair @ ( esk1_4 @ X29 @ X30 @ X31 @ X32 ) @ ( esk2_4 @ X29 @ X30 @ X31 @ X32 ) ) @ X31 )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ~ ( X32 @ ( kpair @ ( esk1_4 @ X29 @ X30 @ X31 @ X32 ) @ ( esk2_4 @ X29 @ X30 @ X31 @ X32 ) ) )
| ~ ( in @ X35 @ X31 )
| ( X32 @ X35 )
| ~ ( subset @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ~ ( in @ X40 @ esk3_0 )
| ~ ( in @ X41 @ esk4_0 )
| ~ ( in @ ( kpair @ X40 @ X41 ) @ esk5_0 )
| ( epred1_0 @ ( kpair @ X40 @ X41 ) ) )
& ( in @ esk6_0 @ esk5_0 )
& ~ ( epred1_0 @ esk6_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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X5 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X5 ) ) @ X3 )
| ( X5 @ X4 )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
in @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ X3 @ X5 ) @ X1 )
| ( X5 @ X4 )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ X3 @ X5 ) @ X2 )
| ( X5 @ X4 )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X5: $i > $o,X2: $i] :
( ( in @ ( kpair @ ( esk1_4 @ X1 @ X2 @ esk5_0 @ X5 ) @ ( esk2_4 @ X1 @ X2 @ esk5_0 @ X5 ) ) @ esk5_0 )
| ( X5 @ esk6_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,negated_conjecture,
subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X5: $i > $o,X2: $i] :
( ( in @ ( esk1_4 @ X1 @ X2 @ esk5_0 @ X5 ) @ X1 )
| ( X5 @ esk6_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X5: $i > $o,X2: $i] :
( ( in @ ( esk2_4 @ X1 @ X2 @ esk5_0 @ X5 ) @ X2 )
| ( X5 @ esk6_0 )
| ~ ( subset @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred1_0 @ ( kpair @ X1 @ X2 ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_17,negated_conjecture,
! [X5: $i > $o] :
( ( in @ ( kpair @ ( esk1_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ ( esk2_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) ) @ esk5_0 )
| ( X5 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,negated_conjecture,
! [X5: $i > $o] :
( ( in @ ( esk1_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ esk3_0 )
| ( X5 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
thf(c_0_19,negated_conjecture,
! [X5: $i > $o] :
( ( in @ ( esk2_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ esk4_0 )
| ( X5 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X5: $i > $o,X4: $i,X3: $i,X2: $i] :
( ( X5 @ X4 )
| ~ ( X5 @ ( kpair @ ( esk1_4 @ X1 @ X2 @ X3 @ X5 ) @ ( esk2_4 @ X1 @ X2 @ X3 @ X5 ) ) )
| ~ ( in @ X4 @ X3 )
| ~ ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_21,negated_conjecture,
! [X5: $i > $o] :
( ( epred1_0 @ ( kpair @ ( esk1_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) @ ( esk2_4 @ esk3_0 @ esk4_0 @ esk5_0 @ X5 ) ) )
| ( X5 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).
thf(c_0_22,negated_conjecture,
~ ( epred1_0 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13])]),c_0_22]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_9]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU682^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 14:08:03 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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.aJc1Bnqmp8/E---3.1_159540.p
% 0.08/0.14 % Version: 3.5.1-ho
% 0.08/0.14 % Preprocessing class: HSSSSMSSSLSNSSA.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting sh5l with 300s (1) cores
% 0.08/0.14 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.14 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.14 % new_ho_10 with pid 159553 completed with status 0
% 0.08/0.14 % Result found by new_ho_10
% 0.08/0.14 % Preprocessing class: HSSSSMSSSLSNSSA.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HGUNF-FFSF33-SSSFMMBN
% 0.08/0.14 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.14 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.14 % Starting new_ho_10 with 901s (1) cores
% 0.08/0.14 % Starting sh5l with 151s (1) cores
% 0.08/0.14 % Starting new_bool_1 with 151s (1) cores
% 0.08/0.14 % Starting new_bool_2 with 146s (1) cores
% 0.08/0.14 % sh5l with pid 159562 completed with status 0
% 0.08/0.14 % Result found by sh5l
% 0.08/0.14 % Preprocessing class: HSSSSMSSSLSNSSA.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HGUNF-FFSF33-SSSFMMBN
% 0.08/0.14 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.14 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.14 % Starting new_ho_10 with 901s (1) cores
% 0.08/0.14 % Starting sh5l with 151s (1) cores
% 0.08/0.14 % Preprocessing time : 0.001 s
% 0.08/0.14 % Presaturation interreduction done
% 0.08/0.14
% 0.08/0.14 % Proof found!
% 0.08/0.14 % SZS status Theorem
% 0.08/0.14 % SZS output start CNFRefutation
% See solution above
% 0.08/0.14 % Parsed axioms : 9
% 0.08/0.14 % Removed by relevancy pruning/SinE : 0
% 0.08/0.14 % Initial clauses : 14
% 0.08/0.14 % Removed in clause preprocessing : 6
% 0.08/0.14 % Initial clauses in saturation : 8
% 0.08/0.14 % Processed clauses : 26
% 0.08/0.14 % ...of these trivial : 0
% 0.08/0.14 % ...subsumed : 0
% 0.08/0.14 % ...remaining for further processing : 26
% 0.08/0.14 % Other redundant clauses eliminated : 0
% 0.08/0.14 % Clauses deleted for lack of memory : 0
% 0.08/0.14 % Backward-subsumed : 1
% 0.08/0.14 % Backward-rewritten : 0
% 0.08/0.14 % Generated clauses : 20
% 0.08/0.14 % ...of the previous two non-redundant : 18
% 0.08/0.14 % ...aggressively subsumed : 0
% 0.08/0.14 % Contextual simplify-reflections : 2
% 0.08/0.14 % Paramodulations : 19
% 0.08/0.14 % Factorizations : 0
% 0.08/0.14 % NegExts : 0
% 0.08/0.14 % Equation resolutions : 0
% 0.08/0.14 % Disequality decompositions : 0
% 0.08/0.14 % Total rewrite steps : 1
% 0.08/0.14 % ...of those cached : 0
% 0.08/0.14 % Propositional unsat checks : 0
% 0.08/0.14 % Propositional check models : 0
% 0.08/0.14 % Propositional check unsatisfiable : 0
% 0.08/0.14 % Propositional clauses : 0
% 0.08/0.14 % Propositional clauses after purity: 0
% 0.08/0.14 % Propositional unsat core size : 0
% 0.08/0.14 % Propositional preprocessing time : 0.000
% 0.08/0.14 % Propositional encoding time : 0.000
% 0.08/0.14 % Propositional solver time : 0.000
% 0.08/0.14 % Success case prop preproc time : 0.000
% 0.08/0.14 % Success case prop encoding time : 0.000
% 0.08/0.14 % Success case prop solver time : 0.000
% 0.08/0.14 % Current number of processed clauses : 17
% 0.08/0.14 % Positive orientable unit clauses : 2
% 0.08/0.14 % Positive unorientable unit clauses: 0
% 0.08/0.14 % Negative unit clauses : 1
% 0.08/0.14 % Non-unit-clauses : 14
% 0.08/0.14 % Current number of unprocessed clauses: 8
% 0.08/0.14 % ...number of literals in the above : 31
% 0.08/0.14 % Current number of archived formulas : 0
% 0.08/0.14 % Current number of archived clauses : 9
% 0.08/0.14 % Clause-clause subsumption calls (NU) : 24
% 0.08/0.14 % Rec. Clause-clause subsumption calls : 11
% 0.08/0.14 % Non-unit clause-clause subsumptions : 3
% 0.08/0.14 % Unit Clause-clause subsumption calls : 0
% 0.08/0.14 % Rewrite failures with RHS unbound : 0
% 0.08/0.14 % BW rewrite match attempts : 0
% 0.08/0.14 % BW rewrite match successes : 0
% 0.08/0.14 % Condensation attempts : 26
% 0.08/0.14 % Condensation successes : 0
% 0.08/0.14 % Termbank termtop insertions : 3502
% 0.08/0.14 % Search garbage collected termcells : 426
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.004 s
% 0.08/0.14 % System time : 0.002 s
% 0.08/0.14 % Total time : 0.006 s
% 0.08/0.14 % Maximum resident set size: 3636 pages
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.011 s
% 0.08/0.14 % System time : 0.009 s
% 0.08/0.14 % Total time : 0.020 s
% 0.08/0.14 % Maximum resident set size: 4864 pages
% 0.08/0.14 % E exiting
%------------------------------------------------------------------------------