%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET611^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:22:12 AM UTC 2026
% Result : Theorem 0.24s 0.28s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 10 equ; 0 cnn)
% Maximal formula atoms : 84 ( 5 avg)
% Number of connectives : 344 ( 77 ~; 102 |; 23 &; 137 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 14 ^; 18 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
emptyset: $i > $o ).
thf(decl_30,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_37,type,
epred1_0: $i > $o ).
thf(decl_38,type,
epred2_0: $i > $o ).
thf(decl_39,type,
esk1_0: $i ).
thf(decl_40,type,
esk2_0: $i ).
thf(thm,conjecture,
! [X22: $i > $o,X23: $i > $o] :
( ( ( intersection @ X22 @ X23 )
= emptyset )
<=> ( ( setminus @ X22 @ X23 )
= X22 ) ),
file('/export/starexec/sandbox/tmp/tmp.qO8gofFiTw/E---3.1_2863547.p',thm) ).
thf(emptyset,axiom,
( emptyset
= ( ^ [X1: $i] : ~ $true ) ),
file('/export/starexec/sandbox/tmp/tmp.qO8gofFiTw/E---3.1_2863547.p',emptyset) ).
thf(intersection,axiom,
( intersection
= ( ^ [X9: $i > $o,X10: $i > $o,X4: $i] :
( ( X9 @ X4 )
& ( X10 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qO8gofFiTw/E---3.1_2863547.p',intersection) ).
thf(setminus,axiom,
( setminus
= ( ^ [X11: $i > $o,X12: $i > $o,X4: $i] :
( ( X11 @ X4 )
& ~ ( X12 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qO8gofFiTw/E---3.1_2863547.p',setminus) ).
thf(c_0_4,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o] :
( ( ( intersection @ X22 @ X23 )
= emptyset )
<=> ( ( setminus @ X22 @ X23 )
= X22 ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_5,plain,
( emptyset
= ( ^ [Z0: $i] : ~ $true ) ),
inference(fof_simplification,[status(thm)],[emptyset]) ).
thf(c_0_6,plain,
( intersection
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[intersection]) ).
thf(c_0_7,plain,
( setminus
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[setminus]) ).
thf(c_0_8,negated_conjecture,
~ ! [X22: $i > $o,X23: $i > $o] :
( ! [X26: $i] :
( ( ( X22 @ X26 )
& ( X23 @ X26 ) )
<=> ~ $true )
<=> ! [X27: $i] :
( ( ( X22 @ X27 )
& ~ ( X23 @ X27 ) )
<=> ( X22 @ X27 ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,c_0_5]),c_0_6]),c_0_7])]) ).
thf(c_0_9,negated_conjecture,
! [X32: $i,X33: $i] :
( ( ~ ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 )
| $true )
& ( ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 )
| $true )
& ( ~ ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 )
| ~ ( epred2_0 @ esk1_0 )
| $true )
& ( ~ ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 )
| ~ $true )
& ( ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 )
| ~ $true )
& ( ~ ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 )
| ~ $true )
& ( ~ ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ~ $true )
& ( ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ~ $true )
& ( ~ ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ~ $true )
& ( ~ ( epred1_0 @ X33 )
| ( epred2_0 @ X33 )
| ( epred1_0 @ X33 )
| ~ ( epred1_0 @ X32 )
| ~ ( epred2_0 @ X32 )
| ~ $true )
& ( ( epred1_0 @ X33 )
| ~ ( epred1_0 @ X33 )
| ~ ( epred1_0 @ X32 )
| ~ ( epred2_0 @ X32 )
| ~ $true )
& ( ~ ( epred2_0 @ X33 )
| ~ ( epred1_0 @ X33 )
| ~ ( epred1_0 @ X32 )
| ~ ( epred2_0 @ X32 )
| ~ $true )
& ( ~ ( epred1_0 @ X33 )
| ( epred2_0 @ X33 )
| ( epred1_0 @ X33 )
| ( epred1_0 @ X32 )
| $true )
& ( ( epred1_0 @ X33 )
| ~ ( epred1_0 @ X33 )
| ( epred1_0 @ X32 )
| $true )
& ( ~ ( epred2_0 @ X33 )
| ~ ( epred1_0 @ X33 )
| ( epred1_0 @ X32 )
| $true )
& ( ~ ( epred1_0 @ X33 )
| ( epred2_0 @ X33 )
| ( epred1_0 @ X33 )
| ( epred2_0 @ X32 )
| $true )
& ( ( epred1_0 @ X33 )
| ~ ( epred1_0 @ X33 )
| ( epred2_0 @ X32 )
| $true )
& ( ~ ( epred2_0 @ X33 )
| ~ ( epred1_0 @ X33 )
| ( epred2_0 @ X32 )
| $true ) ),
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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
( ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i] :
( ~ ( epred2_0 @ X1 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred1_0 @ X3 )
| ~ ( epred2_0 @ X3 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,negated_conjecture,
( ( epred1_0 @ esk1_0 )
| ( epred1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ( epred2_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ~ ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i,X1: $i] :
( ~ ( epred1_0 @ X3 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[c_0_12]) ).
thf(c_0_18,negated_conjecture,
( ( epred2_0 @ esk2_0 )
| ( epred1_0 @ esk1_0 ) ),
inference(csr,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_19,negated_conjecture,
( ( epred2_0 @ esk1_0 )
| ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ esk2_0 ) ),
inference(cn,[status(thm)],[c_0_15]) ).
thf(c_0_20,negated_conjecture,
( ( epred1_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(cn,[status(thm)],[c_0_16]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk1_0 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]) ).
thf(c_0_22,negated_conjecture,
( ( epred2_0 @ esk2_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(csr,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_23,negated_conjecture,
epred1_0 @ esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_14]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i] :
( ( epred2_0 @ esk2_0 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_22]),c_0_23])]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ esk2_0 )
| ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_23])]) ).
thf(c_0_26,negated_conjecture,
epred2_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
thf(c_0_27,negated_conjecture,
epred1_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_23])]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i] :
( ~ ( epred1_0 @ X1 )
| ~ ( epred2_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_27])]) ).
thf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET611^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 13:39:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.09/0.26 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.qO8gofFiTw/E---3.1_2863547.p
% 0.24/0.28 % Version: 3.5.1-ho
% 0.24/0.28 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.28 % Starting sh1l with 300s (1) cores
% 0.24/0.28 % Starting post_as_ho10 with 300s (1) cores
% 0.24/0.28 % post_as_ho1 with pid 2863561 completed with status 0
% 0.24/0.28 % Result found by post_as_ho1
% 0.24/0.28 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.28 % No SInE strategy applied
% 0.24/0.28 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % SubtermCWHack with pid 2863565 completed with status 0
% 0.24/0.28 % Result found by SubtermCWHack
% 0.24/0.28 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.24/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.24/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.24/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.28 % No SInE strategy applied
% 0.24/0.28 % Search class: HGHNF-FFSF00-SHSSMFNN
% 0.24/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.28 % Preprocessing time : 0.001 s
% 0.24/0.28
% 0.24/0.28 % Proof found!
% 0.24/0.28 % SZS status Theorem
% 0.24/0.28 % SZS output start CNFRefutation
% See solution above
% 0.24/0.28 % Parsed axioms : 29
% 0.24/0.28 % Removed by relevancy pruning/SinE : 0
% 0.24/0.28 % Initial clauses : 32
% 0.24/0.28 % Removed in clause preprocessing : 25
% 0.24/0.28 % Initial clauses in saturation : 7
% 0.24/0.28 % Processed clauses : 14
% 0.24/0.28 % ...of these trivial : 0
% 0.24/0.28 % ...subsumed : 2
% 0.24/0.28 % ...remaining for further processing : 12
% 0.24/0.28 % Other redundant clauses eliminated : 0
% 0.24/0.28 % Clauses deleted for lack of memory : 0
% 0.24/0.28 % Backward-subsumed : 2
% 0.24/0.28 % Backward-rewritten : 6
% 0.24/0.28 % Generated clauses : 13
% 0.24/0.28 % ...of the previous two non-redundant : 9
% 0.24/0.28 % ...aggressively subsumed : 0
% 0.24/0.28 % Contextual simplify-reflections : 4
% 0.24/0.28 % Paramodulations : 13
% 0.24/0.28 % Factorizations : 0
% 0.24/0.28 % NegExts : 0
% 0.24/0.28 % Equation resolutions : 0
% 0.24/0.28 % Disequality decompositions : 0
% 0.24/0.28 % Total rewrite steps : 14
% 0.24/0.28 % ...of those cached : 11
% 0.24/0.28 % Propositional unsat checks : 0
% 0.24/0.28 % Propositional check models : 0
% 0.24/0.28 % Propositional check unsatisfiable : 0
% 0.24/0.28 % Propositional clauses : 0
% 0.24/0.28 % Propositional clauses after purity: 0
% 0.24/0.28 % Propositional unsat core size : 0
% 0.24/0.28 % Propositional preprocessing time : 0.000
% 0.24/0.28 % Propositional encoding time : 0.000
% 0.24/0.28 % Propositional solver time : 0.000
% 0.24/0.28 % Success case prop preproc time : 0.000
% 0.24/0.28 % Success case prop encoding time : 0.000
% 0.24/0.28 % Success case prop solver time : 0.000
% 0.24/0.28 % Current number of processed clauses : 4
% 0.24/0.28 % Positive orientable unit clauses : 3
% 0.24/0.28 % Positive unorientable unit clauses: 0
% 0.24/0.28 % Negative unit clauses : 0
% 0.24/0.28 % Non-unit-clauses : 1
% 0.24/0.28 % Current number of unprocessed clauses: 0
% 0.24/0.28 % ...number of literals in the above : 0
% 0.24/0.28 % Current number of archived formulas : 0
% 0.24/0.28 % Current number of archived clauses : 8
% 0.24/0.28 % Clause-clause subsumption calls (NU) : 11
% 0.24/0.28 % Rec. Clause-clause subsumption calls : 10
% 0.24/0.28 % Non-unit clause-clause subsumptions : 7
% 0.24/0.28 % Unit Clause-clause subsumption calls : 3
% 0.24/0.28 % Rewrite failures with RHS unbound : 0
% 0.24/0.28 % BW rewrite match attempts : 3
% 0.24/0.28 % BW rewrite match successes : 3
% 0.24/0.28 % Condensation attempts : 0
% 0.24/0.28 % Condensation successes : 0
% 0.24/0.28 % Termbank termtop insertions : 1905
% 0.24/0.28 % Search garbage collected termcells : 352
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.004 s
% 0.24/0.28 % System time : 0.003 s
% 0.24/0.28 % Total time : 0.007 s
% 0.24/0.28 % Maximum resident set size: 3656 pages
% 0.24/0.28
% 0.24/0.28 % -------------------------------------------------
% 0.24/0.28 % User time : 0.006 s
% 0.24/0.28 % System time : 0.007 s
% 0.24/0.28 % Total time : 0.014 s
% 0.24/0.28 % Maximum resident set size: 4608 pages
% 0.24/0.28 % E exiting
%------------------------------------------------------------------------------